Program and Abstracts

Algebra

⋅ 28th-A-09:00 − 09:05 {\scriptsize \rm [Contributed Talk(5min)+Poster Session(30min)]} Differential equations associated with higher-order Frobenius–Euler numbers revisited (Taekyun Kim, Dae San Kim, Lee-Chae Jang, Hyuck In Kwon )

김태균((광운대)), 김대산((서강대)), 장이채((건국대)), 권혁인*((광운대))
Taekyun Kim, Kwangwoon University, Dae San Kim, Sogang University, Lee-Chae Jang, Konkuk University, Hyuck In Kwon*, Kwangwoon University

In this talk, we derive differential equations from the generating function of higher-order Frobenius–Euler numbers. In addition, we give some new and explicit identities for higher-order Frobenius–Euler numbers arising from those differential equations.

2010 Mathematics Subject Classification: 05A19, 11B83, 34A30
Key Words and Phrases: higher-order Frobenius–Euler numbers, higher-order Euler numbers, differential equation

⋅ 28th-A-09:05 − 09:10 {\scriptsize \rm [Contributed Talk(5min)+Poster Session(30min)]} Some identities of Fubini polynomials arising from differential equations (Gwan Woo Jang)

장관우((광운대))
Gwan Woo Jang, Kwang Woon University

Recently, Kim-Kim have studied Fubini polynomials, which are related to Stirling numbers of the second kind. In this paper, we study the differential equation arising from the generating function of Fubini polynomials and we derive some new interesting identities and properties from our differential equations.

2010 Mathematics Subject Classification: 11B68, 11S80
Key Words and Phrases: Fubini polynomials

⋅ 28th-A-09:10 − 09:15 {\scriptsize \rm [Contributed Talk(5min)+Poster Session(30min)]} Minimal complex surfaces of general type with $K^2=7,8$ and $p_g=q=2$ (Yoonjeong Yang)

양윤정((충남대))
Yoonjeong Yang, Chungnam National University

I construct minimal complex surfaces of general type with $K^2=7,8$ and $p_g=q=2$ as branched double coverings of Enriques surfaces. In order to get these examples we need certain branch divisors on Enriques surface coming from some divisors of bidegree $(1,4)$ on $\mathbb{P}^1\times\mathbb{P}^1$.

2010 Mathematics Subject Classification: 14J29
Key Words and Phrases: complex surface, general type, $K^2=7,8$, $p_g=q=2$, double covering, Enriques surface, $\mathbb{P}^1\times\mathbb{P}^1$

⋅ 28th-A-09:15 − 09:20 {\scriptsize \rm [Contributed Talk(5min)+Poster Session(30min)]} A generalization of Armendariz and NI properties (Dan Li, Zhelin Piao, Sang Jo Yun)

Dan Li*((부산대)), Zhelin Piao((부산대)), 윤상조((부산대))
Dan Li*, Pusan National University, Zhelin Piao, Pusan National University, Sang Jo Yun, Pusan National University

Antoine showed that the properties of Armendariz and NI are independent of each other. The study of Armendariz and NI rings has been doing important roles in the research of zero-divisors in noncommutative ring theory. In this article we concern a new class of rings which generalizes both Armendariz and NI rings. The structure of such sort of ring is investigated in relation with near concepts and ordinary ring extensions. Necessary examples are examined in the procedure

2010 Mathematics Subject Classification: 16N40, 16S36, 16U80, 16D25
Key Words and Phrases: IPN ring, NI ring, Armendariz ring, polynomial ring, matrix ring, Abelian ring

⋅ 28th-A-09:20 − 09:40 Crystals and Schur $P$-positive expansions (Seung Il Choi, Jae-Hoon Kwon)

최승일*((서울대)), 권재훈((서울대))
Seung Il Choi*, Seoul National University, Jae-Hoon Kwon, Seoul National University

We give a new characterization of Littlewood-Richardson-Stembridge tableaux for Schur $P$-functions by using the theory of $\mathfrak{q}(n)$-crystals. We also give alternate proofs of the Schur $P$-expansion of a skew Schur function due to Ardila and Serrano, and the Schur expansion of a Schur $P$-function due to Stembridge using the associated crystal structures.

2010 Mathematics Subject Classification: 05E10, 17B37
Key Words and Phrases: Schur P-function, crystals, Littlewood-Richardson rule

⋅ 28th-A-09:50 − 10:10 Newton--Okounkov bodies of flag Bott--Samelson varieties (Naoki Fujita, Eunjeong Lee, Dong Youp Suh)

Naoki Fujita((Tokyo Institute of Technology)), 이은정*((한국과학기술원)), 서동엽((한국과학기술원))
Naoki Fujita, Tokyo Institute of Technology, Eunjeong Lee*, KAIST, Dong Youp Suh, KAIST

Let $G$ be a simply-connected semisimple algebraic group over $\mathbb{C}$. A Bott--Samelson variety $Z$ is an iterated sequence of $\mathbb{C} P^1$-bundles which has an action of the Borel subgroup $B\subset G$. It is known that the set of holomorphic sections of a holomorphic line bundle $\mathcal L$ over $Z$ is a $B$-module, called a generalized Demazure module. Moreover with an appropriate choice of a valuation $v$, one can construct Newton--Okounkov body associated to $(Z, \mathcal L, v)$ which coincides with a generalized string polytope. In this talk, we introduce flag Bott--Samelson variety, which is a generalization of both Bott--Samelson variety and full flag variety, and moreover, as differentiable manifolds a flag Bott--Samelson variety can be considered as a flag Bott tower which has been introduced recently. Furthermore we study representation theoretic meanings of flag Bott--Samelson varieties. This talk is based on an on-going project with Naoki Fujita and Dong Youp Suh.

2010 Mathematics Subject Classification: 05E10, 14M15
Key Words and Phrases: flag Bott--Samelson varieties, generalized Demazure module, Newton--Okounkov bodies, flag Bott tower

⋅ 28th-A-10:10 − 10:30 Completely positive matrix rank and its linear preservers (Seok-Zun Song)

송석준((제주대))
Seok-Zun Song, Jeju National University

Let $M_{mn}(R)$ denote the set of $m$ by $n$ matrices with entries in real numbers. We write $M_{mn}(R_+ )$ to denote the subset of $M_{mn}(R)$, all of whose entries are nonnegative. Let $S_{n}(R)$ denote the set of all $n$ by $n$ real symmetric matrices. $A$ matrix $A$ in $S_{n}(R)$ is said to be completely positive if there is some matrix $B$ in $M_{n,k}(R_+)$ such that $A=BB^t$. The CP-rank of the matrix $A$ is the smallest $k$ such that $A=BB^t$ for some $B$ in $M_{n,k}(R_+ )$. In this talk, we shall investigate the linear operators on $S_{n}(R)$ that preserve sets of matrices defined by the CP-rank. We classify those that preserve the CP-rank function, those that preserve the set of CP-rank-1 matrices, those that preserve the sets of CP-rank-1 matrices and the set of CP-rank-2 matrices, and those that strongly preserve the set of CP-rank-1 matrices.

2010 Mathematics Subject Classification: 15A04, 15A86
Key Words and Phrases: completely positive matrix, CP-rank, linear operator, (strong) linear preserver

⋅ 28th-B-10:40 − 11:00 Additive uniqueness of almost primes (Poo-Sung Park)

박부성((경남대))
Poo-Sung Park, Kyungnam University

In 1992 C. Spiro showed that if a multiplicative function $f$ satisfies $f(p+q) = f(p)+f(q)$ for all primes $p$ and $q$ and $f(p_0)$ does not vanish at some prime $p_0$, then $f$ is the identity function. In this article we extend Spiro's result to products of exactly $k$ prime factors with multiplicity, which are called $k$-almost primes. That is, if a multiplicative function $f$ satisfies $f(P+Q) = f(P)+f(Q)$ for all $k$-almost primes $P$ and $Q$ and $f(n_0)$ does not vanish at some $k$-almost prime $n_0$, then $f$ is the identity function.

2010 Mathematics Subject Classification: 11A25
Key Words and Phrases: additive uniqueness, multiplicative function, functional equation

⋅ 28th-B-11:00 − 11:20 Matrices related to the Mertens function (Gi-Sang Cheon, Hana Kim)

천기상((성균관대)), 김하나*((성균관대))
Gi-Sang Cheon, Sungkyunkwan University, Hana Kim*, Sungkyunkwan University

The Redheffer matrix $R_n$ is defined as an $n\times n$ matrix whose $(i,j)$-entry is 1 if either $j=1$ or $i$ divides $j$, and $0$ otherwise. Asymptotic behavior of the determinant of the Redheffer matrix $M(n)=\sum_{k=0}^n \mu(k)$, which is called the Mertens function, is known to be closely related to the Riemann hypothesis. In this talk, we introduce an infinite family of matrices using Riordan matrices in which each has the same determinant as the Redheffer matrix. A Riordan matrix is an infinite lower triangular matrix whose $(i,j)$-entry is the coefficient of $z^i$ in $g(z)f(z)^j$ for $i,j\ge0$, where $g(z)$ and $f(z)$ are formal power series satisfying $g(0)=1$, $f(0)=0$ and $f^\prime(0)=1$. We find the generating function for the characteristic polynomials of the new matrices and a sufficient condition for the Riemann hypothesis using the singular values of the new matrices.

2010 Mathematics Subject Classification: 11M26, 15A18
Key Words and Phrases: Redheffer matrix, Riordan matrix, equimodular matrices, singular values

⋅ 28th-B-11:30 − 11:50 Infinite families of irregular primes in cyclotomic function fields (Jungyun Lee, Yoonjin Lee)

이정연*((이화여대)), 이윤진((이화여대))
Jungyun Lee*, Ewha Womans University, Yoonjin Lee, Ewha Womans University

We find two types of infinite families of irregular primes $f$ for which the divisor class numbers of the maximal real cyclotomic function fields $k(\Lambda_f)^+$ with conductor $f$ are divisible by $N$. For the first family of irregular primes, $N$ is a power of a prime $p$, and for the second family of irregular primes, $N$ is a composite number $(p \ell)^5 $ for a prime $\ell$ different from a prime $p$. Furthermore, in the former case, we obtain the result on the lower bound of the $p$-rank of the divisor class group of $k(\Lambda_f)^+$.

2010 Mathematics Subject Classification: 11R29, 11R58
Key Words and Phrases: irregular prime, regulator, function field, sextic extension

⋅ 28th-B-11:50 − 12:10 The locations of the zeros of certain weakly holomorphic modular forms and relations between the zeros (SoYoung Choi, Bo-Hae Im)

최소영*((경상대)), 임보해((한국과학기술원))
SoYoung Choi*, Gyeongsang National University, Bo-Hae Im, KAIST

For a complex-valued function, it is natural to find the location of the zeros of the function. It is one of the most famous problems to whether the nontrivial zeros of the Riemann zeta function lie on a particular vertical line. In the modular form theory, the easiest examples that is known about the locations of the zeros are the Eisenstein series for the full modular group. Indeed, the zeros in the fundamental domain of the functions lie on a unit circle. In this talk, we study the locations of the zeros of certain weakly holomorphic modular forms. And we investigate relations between the zeros of the functions. This is a joint work with Bo-Hae Im.

2010 Mathematics Subject Classification: 11F03, 11F11
Key Words and Phrases: the zeros of weakly holomorphic modular forms

⋅ 28th-C-14:10 − 14:30 The Oort-Tate cyclic group scheme of order $p$ and Godeaux surfaces (Soon Young Kim, Miles Reid)

김순영*((서강대)), Miles Reid((University of Warwick))
Soon Young Kim*, University of Sogang, Miles Reid, University of Warwick

We study the cyclic group scheme $C_p$ of order $p$ due to Oort and Tate. In this talk we apply it to give a uniform construction of the Godeaux surfaces with $Pic^\tau$ of order $5$. This is joint work in progress with Miles Reid.

2010 Mathematics Subject Classification: 14J29
Key Words and Phrases: Godeaux surfaces, cyclic group scheme

⋅ 28th-C-14:30 − 14:50 A characterization of Inoue surfaces with $p_g=0$ and $K^2=7$ (Yifan Chen, YongJoo Shin)

Yifan Chen((Beihang University)), 신용주*((카이스트))
Yifan Chen, Beihang University, YongJoo Shin*, KAIST

Let $S$ be a minimal complex surface of general type with $p_g=0$, $K^2=7$ and having an involution $\sigma$. In this talk, we show that, if the divisorial part of the fixed locus of $\sigma$ consists of two irreducible components $R_1$ and $R_2$, with $g(R_1)=3,\ R_1^2=0,\ g(R_2)=2$ and $R_2^2=-1$, then the Klein group $\mathbb{Z}_2\times \mathbb{Z}_2$ acts faithfully on $S$ and $S$ is indeed an Inoue surface.

2010 Mathematics Subject Classification: 14J29
Key Words and Phrases: Inoue surface, involution, of general type

⋅ 28th-C-14:50 − 15:10 The regularity of partial elimination ideals, Castelnuovo normality and syzygies (Jeaman Ahn, Sijong Kwak)

안재만*((공주대)), 곽시종((공주대))
Jeaman Ahn*, Kongju National University, Sijong Kwak, Kongju National University

Let $X$ be a reduced closed subscheme in $\mathbb P^n$, $\pi: X\to Y=\pi(X) \subset \mathbb P^{n-1}$ be a generic projection and $Z_i(X)$ be the closed subscheme of $Y$ defined by the $i$-th partial elimination ideal $K_i(I_X)$ of $X$, which is supported on the $i$-th multiple point locus of $\pi$. The goal of this paper is to explore syzygy behaviors and Castelnuovo normalities of the projection $Y$ with respect to the algebraic property of multiple loci $Z_i(X)$ (or $K_i(I_X)$) of $\pi$. It is known that if $X$ is irreducible and $Z_i(X)\neq \emptyset$, then $\text{reg}(Z_i(X))=\text{reg}(K_i(X))$. As a main result, we prove that $(d-i)$-regularity of $K_i(I_X)$ for all $i\geq 1$ implies the followings: \begin{itemize} \item[(a)] $H^1(\mathcal I_X(d))=H^1(I_Y(d))$ and, \item[(b)] if $X$ satisfies property $\text{\bf N}_{d,p}$ for $p\geq 2$, then $Y$ satisfies property $\text{\bf N}_{d+1,p-1}$. \end{itemize} We give some results as an application on the syzygies and higher normality of $Y$ when $X$ satisfies $\text{\bf N}_{3,p}$ for some $p\geq 2$, which recover and generalize several results. Moreover, if $X\subset \mathbb P(H^0(\mathcal L))$ is projectively normal for a very ample line bundle $\mathcal L$ and $X_W$ is an isomorphic embedding of $X$ in $\mathbb P(W), W\subset H^0(\mathcal L)$, then $X_W$ has the persistence property of Castelnuovo normality, i.e., if $X_W$ is $d$-normal then $X_W$ is $k$-normal for all $k\geq d$.

2010 Mathematics Subject Classification: 14N05, 13D02
Key Words and Phrases: syzygy, Castelnuovo normalities, Castelnuovo Mumford regularity, partial elimination ideals, projections

⋅ 29th-D-09:00 − 09:20 The complete decomposition on piecewise prime modules (Gangyong Lee, S. Tariq Rizvi)

이강용*((충남대)), S. Tariq Rizvi((The Ohio State University at Lima))
Gangyong Lee*, Chungnam National University, S. Tariq Rizvi, The Ohio State University at Lima

The purpose of this talk is to further the study of quasi-Baer modules by investigating the structure of a special class of quasi-Baer modules. As a module theoretic analogue of a piecewise prime ring, we characterize a piecewise prime module (simply, a PWP module) via its endomorphism ring. We provide a complete decomposition theorem for a PWP module as a finite direct sum of endoprime modules, which play a role analogous to that of prime rings in the case of PWP rings. We also show that endoprime submodules are the building blocks of all PWP modules. A module $M$ is called \emph{endoprime} if every nonzero fully invariant submodule is faithful as a left module over its endomorphism ring, equivalently if $\mathbf{l}_S(N)=0$ for all $N \unlhd M$ where $S=\text{End}_R(M)$. We also obtained that every direct summand of a PWP module is a PWP module. It is shown that any direct sum of copies of a PWP module is always a PWP module. Consequently, every column finite matrix ring over a PWP ring is a PWP ring. This is a joint work with S. Tariq Rizvi.

2010 Mathematics Subject Classification: 16D70, 16S50
Key Words and Phrases: quasi-Baer module, endoprime module, piecewise prime ring, piecewise prime module

⋅ 29th-D-09:20 − 09:40 Automorphisms of Weyl algebras (No Ho Myung, Sei Qwon Oh)

명노호*((충남대)), 오세권((충남대))
No Ho Myung*, Chungnam National University, Sei Qwon Oh, Chungnam National University

Kanel-Belov and Kontsevich's conjecture is proved: Automorphisms groups of Weyl algebras are isomorphic to Poisson automorphisms of Poisson Weyl algebras.

2010 Mathematics Subject Classification: 17B63, 16S36
Key Words and Phrases: (Poisson) Weyl algebra, (Poisson) Automorphisms group, Kanel-Belov and Kontsevich's conjecture

⋅ 29th-D-09:50 − 10:10 On matrix rings with skew Hochschild 2-cocycles (Nam Kyun Kim)

김남균((한밭대))
Nam Kyun Kim, Hanbat National University

We study structures of Hochschild 2-cocycles related to endomorphisms and introduce a skew Hochschild 2-cocycle. We moreover define skew Hochschild extensions equipped with skew Hochschild 2-cocycles, and then we examine uniquely clean, Abelian, directly finite, symmetric, and reversible ring properties of skew Hochschild extensions and related ring systems. The results obtained here provide various kinds of examples of such rings. Especially, we give an answer negatively to the question of H. Lin and C. Xi for the corresponding Hochschild extensions of reversible (or semicommutative) rings. Finally, we establish three kinds of Hochschild extensions with Hochschild 2-cocycles and skew Hochschild 2-cocycles.

2010 Mathematics Subject Classification: 16S50, 15A30, 15B33
Key Words and Phrases: skew Hochschild extensions, skew triangular matrix rings, (uniquely) clean rings, symmetric rings
Analysis I

⋅ 29th-D-09:00 − 09:20 A complete characterization of parameters of the discrete $p$-Laplacian nonlinear parabolic equations with $q$-nonlocal reaction with respect to the blow-up property (Jaeho Hwang, Soon-Yeong Chung)

황재호*((서강대)), 정순영((서강대))
Jaeho Hwang*, Sogang University, Soon-Yeong Chung, Sogang University

In this talk, we consider discrete $p$-Laplacian nonlinear parabolic equations with $q$-nonlocal reaction under Dirichlet boundary condition as follows: \begin{equation*} \begin{cases} u_{t}\left(x,t\right) = \Delta_{p,\omega} u\left(x,t\right) +\lambda \sum_{y \in S} \left\vert u\left(x,t\right) \right\vert^{q-1} u\left(x,t\right), &\left(x,t\right) \in S \times \left(0,\infty\right), \\ u\left(x,t\right) = 0, &\left(x,t\right) \in \partial S \times \left(0,\infty\right), \\ u\left(x,0\right) = u_{0} \geq 0, &x \in \overline{S}. \end{cases} \end{equation*} Here, $S$ is a network with boundary $\partial S$. The parameters $p>1$, $q>0$ are completely characterized to see when the solution blows up, vanishes, or exists globally. Indeed, the blow-up rates when blow-up does occur are derived. Also, we give some numerical experiments which explain the main results.

2010 Mathematics Subject Classification: 39A12, 39A13, 39A70, 35K57
Key Words and Phrases: discrete p-Laplacian, semilinear parabolic equation, nonlocal reaction, blow-up

⋅ 29th-D-09:20 − 09:40 A new condition for the concavity method of blow-up solutions to semilinear heat equations (Soon-Yeong Chung, Min Jun Choi )

정순영((서강대)), 최민준*((서강대))
Soon-Yeong Chung, Sogang University, Min Jun Choi*, Sogang University

In this talk, we consider the semilinear heat equations under Dirichlet boundary condition \begin{equation*} \begin{cases} u_{t}\left(x,t\right)=\Delta u\left(x,t\right)+f(u(x,t)), & \left(x,t\right)\in \Omega\times\left(0,+\infty\right),\\ u\left(x,t\right)=0, & \left(x,t\right)\in\partial \Omega\times\left[0,+\infty\right),\\ u\left(x,0\right)=u_{0}\geq0, & x\in\overline{\Omega}, \end{cases} \end{equation*} where $\Omega$ is a bounded domain of $\mathbb{R}^{N}$ $(N\geq1)$ with smooth boundary $\partial\Omega$. The main contribution of our work is to introduce a new condition \[ \alpha \int_{0}^{u}f(s)ds \leq uf(u)+\beta u^{2}+\gamma,\,\,u>0\leqno(C) \] for some $\alpha, \beta, \gamma>0$ with $0<\beta\leq\frac{\left(\alpha-2\right)\lambda_{0}}{2}$, where $\lambda_{0}$ is the first eigenvalue of Laplacian $\Delta$ in order to use the concavity method to obtain the blow-up solutions to the semilinear heat equations. In fact, it will be seen that the condition $(C)$ improves the conditions ever known so far.

2010 Mathematics Subject Classification: 39A14, 35K57
Key Words and Phrases: semilinear heat equations, concavity method, blow-up

⋅ 29th-D-09:50 − 10:10 Several split regular functions valued split quaternion in Clifford analysis (Hang Ul Kang, Jeong Young Cho, Kwang Ho Shon)

강한울*((부산대)), 조정영((부산대)), 손광호((부산대))
Hang Ul Kang*, Pusan National University, Jeong Young Cho, Pusan National University, Kwang Ho Shon, Pusan National University

In this paper, we investigate the regularities of the hypercomplex valued functions of the split quaternion variables. We define several differential operators for the split qunaternionic function. We research several left split regular functions for each differential operators. We also investigate split harmonic functions. And we find the corresponding Cauchy-Riemann system and the corresponding Cauchy theorem for each regular functions on the split quaternion field.

2010 Mathematics Subject Classification: 32A99, 30G35, 11E88
Key Words and Phrases: Clifford analysis, split quaternion, corresponding split Cauchy Riemann system, differential of split quaternionic function, left-differential, split Cauchy theorem

⋅ 29th-D-10:10 − 10:30 Emergent dynamics of the Winfree model with time-delay (Seung-Yeal Ha, Doheon Kim)

하승열((서울대)), 김도헌*((서울대))
Seung-Yeal Ha, Seoul National University, Doheon Kim*, Seoul National University

The Winfree model is the first mathematical model which describes the synchronization phenomenon in an ensemble of weakly coupled limit-cycle oscillators. Time delays in the interactions between the oscillators are induced by the finite propagation speed of information or communication, and generate some oscillatory phenomena in the initial time-layer near the initial time. We provide a sufficient framework for the complete oscillator death of Winfree oscillators in terms of their initial configuration, time delay, and coupling strength.

2010 Mathematics Subject Classification: 70F99, 92B25
Key Words and Phrases: Winfree model, synchronization

⋅ 29th-E-10:40 − 11:00 Critical threshold phenomena for the wave equations (Tae Gab Ha)

하태갑((전북대))
Tae Gab Ha, Chonbuk National University

In this talk, we consider the critical threshold phenomena for the wave equations with boundary damping and source terms. Critical threshold serves to separate the initial data (and boundary data is applicable) into two regimes, one leads to finite time break down (wave breaking, shock formation or blow-up of solution), and the other data lead to global existence. First, we find the critical threshold value and then we will study the global existence and energy decay rates of solution. Also in other regime, that there is no global solutions, we will show the blow-up of solutions in finite time.

2010 Mathematics Subject Classification: 35L05, 35B35
Key Words and Phrases: wave equations, critical threshold

⋅ 29th-E-11:00 − 11:20 KdV flows vs canonical system flows (Injo Hur)

허인조((울산과학기술원))
Injo Hur, UNIST, Ulsan National Institute of Science and Technology

We would like to compare KdV flows to canonical system flows which may be thought of as generalizations of KdV flows. Then we will explore several features of canonical system flows and the (correct) way to connect these two flows.

2010 Mathematics Subject Classification: 35Q53, 37K10
Key Words and Phrases: KdV flows, canonical systems

⋅ 29th-E-11:30 − 11:50 General energy decay for a nonlinear Kirchhoff type equation (Daewook Kim)

김대욱((서원대))
Daewook Kim, Seowon University

This talk is concerned with a nonlinear equation of Kirchhoff type with some boundary conditions in a bounded domain. We prove that, for suitable initial data, the solution exists globally in time. For the energy decay rates, we consider the general nonlinear terms satisfying a smallness conditions. Finally, we prove the general energy decay rate by using perturbed modified energy method.

2010 Mathematics Subject Classification: 35L70
Key Words and Phrases: general energy decay, Kirchhoff type equation, perturbed modified energy method

⋅ 29th-E-11:50 − 12:10 Remarks on Chern-Simons gauged $O(3)$ sigma model in one space dimension (Guanghui Jin, Hyungjin Huh)

김광휘*((National Center for Theoretical Sciences/National Taiwan University)), 허형진((중앙대))
Guanghui Jin*, National Center for Theoretical Sciences/National Taiwan University, Hyungjin Huh, Chung-Ang University

We study an initial value problem of the Chern-Simons gauged $O(3)$ sigma model in one space dimension under the gauge condition $A_1=0$ and find the stationary solutions. We also study low regularity local well-posedness using bilinear estimates for wave-Sobolev space $\mathcal{H}^{s,\,\theta}$.

2010 Mathematics Subject Classification: 35L15, 35L45, 35Q40, 35F25
Key Words and Phrases: Chern-Simons $O(3)$ sigma model, Cauchy problem, stationary solutions, wave-Sobolev space, energy global solution
Analysis II

⋅ 29th-D-09:00 − 09:20 Derivation of quasi-geostropic equation from Navier-Stokes-Fourier system with general initial data (Young-Sam Kwon)

권영삼((동아대))
Young-Sam Kwon, Dong-A University

In this talk we derive the quasi-geostropic equation from Navier-Stokes-Fourier system with general initial data. The tool is based on the relative entropy and dispersive estimates.

2010 Mathematics Subject Classification: 35
Key Words and Phrases: Navier-Stokes-Fourier system

⋅ 29th-D-09:20 − 09:40 Strichartz and smoothing estimates in weighted $L^2$ spaces and their applications (Youngwoo Koh, Ihyeok Seo)

고영우*((공주대)), 서이혁((성균관대))
Youngwoo Koh*, Kongju National University, Ihyeok Seo, Sungkyunkwan University

We study an improved Strichartz estimates for Schrodinger equation weighted $L^2$ spaces. Indeed, we will extend the class of weighted function in the weighed $L^2$ estimate to larger Morry-Campanato class. Also, we will consider the smoothing estimate in weighted spaces.

2010 Mathematics Subject Classification: 35B45
Key Words and Phrases: Strichartz estimates, smoothing estimates, Morrey-Campanato class

⋅ 29th-D-09:50 − 10:10 Radial solutions for the self-dual Maxwell gauged $O(3)$ sigma model coupled with gravitation (Jongmin Han, Ju Hee Son)

한종민((경희대)), 손주희*((경희대))
Jongmin Han, Kyung Hee University, Ju Hee Son*, Kyung Hee University

In this talk, we are concerned with an elliptic system arising from the Einstein equations coupled with the classical sigma model and Abelian gauge fields in space-time. Reducing this system to a single equation and setting up the radial ansatz, we classify solutions into three cases: topological solutions, nontopological solutions of type I, and nontopological solutions of type II.

2010 Mathematics Subject Classification: 35J61
Key Words and Phrases: self-dual Maxwell gauged $O(3)$ sigma model, radially symmetric solutions

⋅ 29th-D-10:10 − 10:30 Existence of non-topological multi-string solutions for a gravitational $O(3)$ gauge field model (Nari Choi, Jongmin Han)

최나리*((경희대)), 한종민((경희대))
Nari Choi*, Kyung Hee University, Jongmin Han, Kyung Hee University

In this paper, we consider the self-dual equations for the Maxwell gauged $O(3)$ sigma model coupled with gravity. We prove the existence of non-topological multi-string solutions and obtain their decay estimates at infinity. Using the decay rates, we compute the static energy, the magnetic flux and the total Gaussian curvature corresponding to our solutions. Our solutions are constructed by a perturbation argument with an application of the Implicit Function Theorem.

2010 Mathematics Subject Classification: 35J61, 35Q75, 81T13
Key Words and Phrases: non-topological solutions, multi-string solutions, gravitational Maxwell gauged $O(3)$ sigma model

⋅ 29th-E-10:40 − 11:00 A new generalized integral operator and its applications (Hyun Soo Chung, Seung Jun Chang)

정현수*((단국대)), 장승준((단국대))
Hyun Soo Chung*, Dankook University, Seung Jun Chang, Dankook University

In this talk, we define a generalized integral operator which has the kernel. This operator is more generalized form rather than the integral operators in previous papers. Furthermore, we establish the existence and some relationships for the generalized integral operator. We then give useful examples with respect to the generalized integral operator. Finally, we give an application which is used in quantum mechanics. Our integral operator contains the kernel. This is the most difference from the previous integral operators on Wiener space.

2010 Mathematics Subject Classification: 60J65, 28C20
Key Words and Phrases: generalized integral operator, kernel of the integral operator, diffusion equation, error function, quantum mechanics

⋅ 29th-E-11:00 − 11:20 A study on degenerate Laplace transform and degenerate Gamma functions (Lee-Chae Jang, Taekyun Kim)

장이채*((건국대)), 김태균((광운대))
Lee-Chae Jang*, Konkuk University, Taekyun Kim, Kwangwoon University

In this paper, we introduce the degenerate Laplace transform and degenerate Gamma function and investigate their properties. By using these properties, we derive some formulas related with to the degenerate Laplace transform and degenerate gamma function. Furthermore, we compute the degenerate Laplace transform of the degenerate trigonometric functions, degenerate hyperbolic functions, and $t^n$.

2010 Mathematics Subject Classification: 11B68, 42A16
Key Words and Phrases: fuzzy measure, Choquet integral, Jensen inequality

⋅ 29th-E-11:30 − 11:50 Rate of convergence towards Hartree dynamics with singular interaction potential (Li Chen, Ji Oon Lee, Jinyeop Lee)

Li Chen((University of Mannheim)), 이지운((한국과학기술원)), 이진엽*((한국과학기술원))
Li Chen, University of Mannheim, Ji Oon Lee, KAIST, Jinyeop Lee*, KAIST

We consider a system of $N$-Bosons with a two-body interaction potential $V \in L^2(\mathbb{R}^3)+L^\infty(\mathbb{R}^3)$, possibly singular than the Coulomb interaction. We show that, with $H^1(\mathbb{R}^3)$ initial data, the difference between the many-body Schr\"odinger evolution in the mean-field regime and the corresponding Hartree dynamics is of order $1/N$, for any fixed time. The $N$-dependence of the bound is optimal.

2010 Mathematics Subject Classification: 81V70, 82C10, 81U30
Key Words and Phrases: many-body system, Hartree dynamics, rate of convergence
Analysis III

⋅ 29th-D-09:00 − 09:20 Remarks on operators which are power similar to complex symmetric operators (Mee-Jung Lee, Eungil Ko, Ji Eun Lee)

이미정*((이화여대)), 고응일((이화여대)), 이지은((세종대))
Mee-Jung Lee*, Ewha Womans University, Eungil Ko, Ewha Womans University, Ji Eun Lee, Sejong University

In this talk, we study properties of operators of power similar to complex symmetric operators. Let $C$ be a fixed conjugation on $\mathcal{H}$. For a complex symmetric operator $R$ with respect to a conjugation $C$, we set $PS_n(R)=\{T\in{\mathcal{L(H)}}: T^n \mbox{ is similar to } R^n \}$ for some positive integer $n$ and $PS(R)=\cup_{n=1}^{\infty}PS_n(R)$. In particular, we focus on the stability of complex symmetric and local spectral properties of operator $T\in PS_{n}(R)$ for some symmetric operator $R$. Using the results, we get the some applications of such operators.

2010 Mathematics Subject Classification: 47B20, 47A10
Key Words and Phrases: similar operator, complex symmetric operator, spectral theory

⋅ 29th-D-09:20 − 09:40 On Hankel and Toeplitz operators, block matrices (Robin Harte, Eungil Ko, Ji Eun Lee)

Robin Harte((Trinity College((Ireland)))), 고응일((이화여대)), 이지은*((세종대))
Robin Harte, Trinity College(Ireland), Eungil Ko, Ewha Womans University, Ji Eun Lee*, Sejong University

Hankel and Toeplitz operators are the compressions of Laurent and bilateral Hankel operators, which in turn can be presented as operator matrices with Toeplitz and Hankel entries. We study properties of Laurent and bilateral Hankel operators.

2010 Mathematics Subject Classification: 47B35, 47A10
Key Words and Phrases: Hankel operator, Toeplitz operator, block matrix

⋅ 29th-D-09:50 − 10:10 A Banach algebra over continuous paths with drifts (Dong Hyun Cho)

조동현((경기대))
Dong Hyun Cho, Kyonggi University

Let $C[0,T]$ denote a generalized analogue of Wiener space, that is, the space of continuous real-valued functions on $[0,T]$, and $C_0[0,T]$ denote the classical Wiener space which is a subspace of $C[0,T]$ satisfying $x(0)=0$ for all $x\in C_0[0,T]$. On this space $C_0[0,T]$, Cameron and Storvick introduced a Banach algebra $\mathcal S$ which is a space of generalized Fourier-Stieltjes transforms of the measures on $L^2[0,T]$. In this talk, we introduce a Banach algebra $S_{\alpha,\beta;\varphi}$ on $C[0,T]$ which is more general than $\mathcal S$, where $\alpha$, $\beta$ and $\varphi$ are the mean function, the variance function and the initial distribution of the paths in $C[0,T]$, respectively. We also investigate its properties, and relationships between it and the Fresnel class which plays a significant role in Feynman integration theories and quantum mechanics.

2010 Mathematics Subject Classification: 28C20
Key Words and Phrases: Banach algebra, continuous path, drift, Feynman integral

⋅ 29th-D-10:10 − 10:30 Behavior of the change of scale for Wiener integrals of unbounded functions (Young Sik Kim)

김영식((한양대))
Young Sik Kim, Hanyang University

We investigate the behavior of the change of scale for Wiener integrals of unbounded functions on the Wiener space.

2010 Mathematics Subject Classification: 28C20
Key Words and Phrases: Wiener integral
Geometry

⋅ 28th-A-09:20 − 09:40 Inequalities for the Casorati curvatures of real hypersurfaces in some Grassmannians (Kwang Soon Park)

박광순((서울시립대))
Kwang Soon Park, University of Seoul

In this talk we obtain two types of optimal inequalities consisting of the normalized scalar curvature and the generalized normalized $\delta$-Casorati curvatures for real hypersurfaces of complex two-plane Grassmannians and complex hyperbolic two-plane Grassmannians. We also obtain the conditions on which the equalities hold.

2010 Mathematics Subject Classification: 53C40, 53C15, 53C26, 53C42
Key Words and Phrases: real hypersurfaces, Grassmannians, scalar curvature, mean curvature, $\delta$-Casorati curvature

⋅ 28th-A-09:40 − 10:00 $C^1$ Hermite interpolation with rational PH curves on the Enneper surface using the M\"obius cubic (Hyun Cheol Lee, Dae Won Yoon)

이현철*((경상대)), 윤대원((경상대))
Hyun Cheol Lee*, Gyeongsang National University, Dae Won Yoon, Gyeongsang National University

In this talk, we show that the geometric and PH-preserving properties of the Enneper surface allow us to find PH interpolants for all regular $C^1$ Hermite data-sets. Each such data-set is satisfied by two scaled Enneper surfaces, and we can obtain four rational interpolants on each surface using the M\"obius cubic.

2010 Mathematics Subject Classification: 65D05
Key Words and Phrases: Pythagorean-hodograph curve, Enneper surface, PH-preserving mapping, $C^1$ Hermite interpolation, M\"obius cubic

⋅ 28th-A-10:10 − 10:30 Standard embeddings of smooth Schubert varieties in $F_4$-homogeneous manifolds (Shin-Young Kim, Kyeong-Dong Park)

김신영((Masaryk University)), 박경동*((기초과학연구원 기하학수리물리연구단))
Shin-Young Kim, Masaryk University, Kyeong-Dong Park*, IBS Center for Geometry and Physics

A rational homogeneous manifold is a homogeneous space $G/P$ for a complex simple Lie group $G$ and a parabolic subgroup $P\subset G$. Under the action of a Borel subgroup $B$ of $G$, the closure of a $B$-orbit in $G/P$ is called a Schubert variety of $G/P$. We characterize standard embeddings of smooth Schubert varieties in rational $F_4$-homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomogeneous smooth Schubert varieties in the 20-dimensional $F_4$-homogeneous manifold associated to a short simple root. As the main ingredients for the proof, we use an analytic continuation along minimal rational curves, the projective second fundamental form and the non-equidimensional Cartan-Fubini type extension theorem.

2010 Mathematics Subject Classification: 53C30, 14M15, 32M10
Key Words and Phrases: smooth Schubert varieties, rational homogeneous manifolds, variety of minimal rational tangents, standard embeddings

⋅ 28th-B-10:40 − 11:00 Hypersurfaces of pseudo-Euclidean spaces satisfying chord properties (Dong-Soo Kim)

김동수((전남대))
Dong-Soo Kim, Chonnam National University

We study hypersurfaces in pseudo-Euclidean space $\mathbb{R}^{n+1}_t$ of arbitrary dimension satisfying the so called chord properties, that is, the Gauss map $G$ on the hypersurface satisfies $\langle y -x, G(x)+G(y)\rangle =0$ identically. First, we show that the Gauss map $G$ satisfies $G(x)=Ax+b$, where $A$ is a self adjoint endomorphism of $\mathbb{R}^{n+1}_t$ and $b$ is a constant vector in $\mathbb{R}^{n+1}_t$. Finally, we give a complete classification theorem for hypersurfaces in pseudo-Euclidean space $\mathbb{R}^{n+1}_t$ satisfying chord properties.

2010 Mathematics Subject Classification: 53C40
Key Words and Phrases: pseudo-Euclidean space, hypersurface, Gauss map, chord property, isoparametric hypersurface

⋅ 28th-B-11:00 − 11:20 Equilibrium points of periodic flows on almost complex, complex, and symplec manifolds (Donghoon Jang)

장동훈((고등과학원))
Donghoon Jang, Korea Institute for Advanced Study

During this talk, we classify and compare periodic flows on almost complex, complex, and symplectic manifolds, when the number of equilibrium points is small (at most 3). This talk is based on the paper `Circle actions on almost complex manifolds with isolated fixed points.' J. Geom. Phys. {\bf 119} (2017), 187--192.

2010 Mathematics Subject Classification: 58C30
Key Words and Phrases: periodic flow, equilibrium point, almost complex manifold, complex manifold, symplectic manifold, weight

⋅ 28th-B-11:30 − 11:50 Hodge structures on generalized complex geometry (Hoil Kim)

김호일((경북대))
Hoil Kim, Kyungpook National University

Generalized complex geometry was introduced to combine complex geometry and symplectic geometry in both parts of mathematics and physics. It is a very useful concept to understand physical duality and mathematical mirror symmetry. In this talk we discuss (noncommutative) Hodge structure on (super) generalized complex manifolds.

2010 Mathematics Subject Classification: 14K10, 14K25, 81T60
Key Words and Phrases: generalized complex structure, Hodge structure, super manifolds, noncommutative, mirror duality

⋅ 28th-C-14:10 − 14:30 The maximal existence condition of Ricci parallel real hypersurfaces in complex Grassmannians of rank two (Chang Hwa Woo, Young Jin Suh)

우창화*((우석대)), 서영진((경북대))
Chang Hwa Woo*, Woosuk University, Young Jin Suh, Kyungpook National University

In this talk, we introduce a notion of parallel Ricci tensor for Hopf hypersurfaces in complex Grassmannians of rank two. We consist partially ordered class from the space spanned by the Reeb vector field to the tangent bunddle of real hypersurfac and try to find the maximal subbundle including Reeb direction which guarantees the existence of real hypersurfaces in the given ambient spaces.

2010 Mathematics Subject Classification: 53C40
Key Words and Phrases: Hadamard manifold, complex Grassmannians of rank two, parallellism, Ricci tensor

⋅ 28th-C-14:30 − 14:50 Real hypersurfaces with recurrent normal Jacobi operator in the complex quadric (Hyunjin Lee, Young Jin Suh)

이현진*((경북대)), 서영진((경북대))
Hyunjin Lee*, Kyungpook National University, Young Jin Suh, Kyungpook National University

In the class of Hermitina symmetric spaces of rank 2, usually we can give examples of Riemannian symmetric spaces $SU_{m+2}/S(U_{2}U_{m})$ and $SU_{m,2}/S(U_{2}U_{m})$, which are said to be complex two-plane Grassmannians and complex hyperbolic two-plane Grassmannians, respectively. In this talk, we will consider the complex quadric $SO_{m+2}/SO_{m}SO_{2}$ as another kind of Hermitian symmetric space with rank 2 of compact type different from the previous ones, which is a complex hypersurface in complex projective space $\mathbb{C}P^{m}$. And it can be regard as a kind of real Grassmann manifold of compact type with rank 2. Accordingly, the complex quadric admits both a complex conjugation structure $A$ and a Kaehler structure $J$, with anti-commutes with each other. By using these structures of the ambient space we classify real hypersurfaces with recurrent normal Jacobi operator in the complex quadric.

2010 Mathematics Subject Classification: 53C40, 53C55
Key Words and Phrases: complex quadric, real hypersurface, Kaehler structure, complex conjugation, recurrent normal Jacobi operator

⋅ 28th-C-14:50 − 15:10 Laplacians and Legendre surfaces in pseudo-Hermitian geometry (Ji-Eun Lee)

이지은((전남대))
Ji-Eun Lee, Chonnam National University

In this talk, we introduce pseudo-Hermitian geometry of Legendre submanifolds in Sasakian space forms. We show that if a Legendre submanifold has $D$-parallel pseudo-Hermitian proper mean curvature vector field in $(2n+1)$-dimensional Sasakian space forms, then $N$ is a Chen submanifold. Here $D$ is the normal connection induced from the Tanaka-Webster connection. Moreover, we find a Legendre surface of 5-dimensional Sasakian space forms such that $\triangle H=\lambda H$ and ${\rm tr}\nabla T(H)=0$ for a constant $\lambda$ with respect to the Tanaka-Webster connection.

2010 Mathematics Subject Classification: 53B25, 53C25
Key Words and Phrases: Sasakian space forms, Legendre surfaces, pseudo-Hermitian geometry
Topology

⋅ 28th-A-09:20 − 09:25 {\scriptsize \rm [Contributed Talk(5min)+Poster Session(30min)]} On 2-cocylces and abelian extensions of a finite quandle (Yongju Bae, Byeorhi Kim)

배용주((경북대)), 김벼리*((경북대))
Yongju Bae, Kyungpook National University, Byeorhi Kim*, Kyungpook National University

Quandle 2-coclye $\phi$ is a function from $Q\times Q$ to an abelian group $A$ satisfying cocycle conditions. In 2003, Carter, Jelsovsky, Kamada, Langford and Saito proved that for a quandle 2-cocylce $\phi$, $X\times A$ became a quandle by $(x,a)*(y,b)=(x*y, a+\phi(x,y))$. In this talk, we will observe the matrices of quandle 2-cocylces and the quandle operation tables of abelian extensions obtained from the cocycle matrices.

2010 Mathematics Subject Classification: 57M25
Key Words and Phrases: quandle, quandle 2-cocycle, abelian extension

⋅ 28th-A-09:25 − 09:30 {\scriptsize \rm [Contributed Talk(5min)+Poster Session(30min)]} On the quandle coloring of $(1,1)$-tangles (Hun Lee, Yongju Bae)

이헌*((경북대)), 배용주((경북대))
Hun Lee*, Kyungpook National University, Yongju Bae, Kyungpook National University

For a quandle $X$, a $(1,1)$-tangle $T$ is $\emph{$X$-colorable}$ if there exists non-trivial coloring map $\textbf{C} : \textbf{A}(T) \rightarrow X$, where $\textbf{A}(T)$ is arcs of $T$. We say that a quandle $X$ is $\emph{end monochromatic}$ for a $(1,1)$-tangle $T$ if any coloring of $T$ by $X$ assigns the same color on the two end arcs [1]. In this talk, we will study some quandles which are end monochromatic for a $(1,1)$-tangle. \medskip \noindent [1] W. Edwin Clark, Masahico Saito, {\it Algebraic properties of quandle extensions and values of cocycle knot invariants}. Journal of Knot Theory and Its Ramifications {\bf 25} (2016), no. 14, 1650080.

2010 Mathematics Subject Classification: 57M25, 57M27
Key Words and Phrases: quandle, coloring, tangle

⋅ 28th-A-09:30 − 09:35 {\scriptsize \rm [Contributed Talk(5min)+Poster Session(30min)]} Upper bound of lattice stick number of spatial graphs (Chaeryn Lee, Seungsang Oh, Hyungkee Yoo)

이채린((고려대)), 오승상((고려대)), 유형기*((고려대))
Chaeryn Lee, Korea University, Seungsang Oh, Korea University, Hyungkee Yoo*, Korea University

The lattice stick number of knots is defined to be the minimal number of straight sticks in the cubic lattice required to construct a lattice stick presentation of the knot. We similarly define the lattice stick number $s_{L}(G)$ of spatial graphs $G$ with vertices of degree at most six (necessary for embedding into the cubic lattice), and present an upper bound in terms of the crossing number $c(G)$ $$ s_{L}(G) \leq 3c(G)+6e-4v-2s+3b+k, $$ where $G$ has $e$ edges, $v$ vertices, $s$ cut-components, $b$ bouquet cut-components, and $k$ knot components.

2010 Mathematics Subject Classification: 57M15, 57M25, 57M27
Key Words and Phrases: lattice stick number, spatial graph

⋅ 28th-A-09:35 − 09:40 {\scriptsize \rm [Contributed Talk(5min)+Poster Session(30min)]} Continuous shadowable points and stability (Sang Jin Kim)

김상진((충남대))
Sang Jin Kim, Chungnam National University

Let $Act(G,X)$ be the set of continuous action of finitely generated group $G$ and compact metric space $X$. In this talk, we study the concepts of topologically stable points and continuous shadowable points of group action $T \in Act(G,X)$. We show that if $T$ is expansive, then the set of continuous shadowable points and topological stable points are coincide. Moreover we show that an expansive action $T\in Act(G,X)$ is topologically stable if and only if every point of $X$ is topologically stable with respect to $T$.

2010 Mathematics Subject Classification: 37B05, 37C50
Key Words and Phrases: group action, shadowing

⋅ 28th-A-09:50 − 10:10 Maximal holonomy of infra-Nilmanifolds with $\mathcal{H}_7(\mathbb{H})$-geometry (Daehwan Koo, Joonkook Shin)

구대환*((대전과학고)), 신준국((충남대))
Daehwan Koo*, Daejeon Science High School for the Gifted, Joonkook Shin, Chungnam National University

In this talk, we study the special Lie group which is called the twisted quaternionic Heisenberg group $\mathcal{H}_7(\mathbb{H}) = \mathbb{R}^3 \tilde\times \mathbb{R}^4$. It is a 7-dimensional nilpotent Lie group with group operation $ (s, \mathbf{x})(t,\mathbf{y}) = (s+t+2\mathcal{I}(\mathbf{x},\mathbf{y}), \mathbf{x}+\mathbf{y}).$ Our aim is to study the 7-dimensional infra-Nilmanifolds modeled on $\mathcal{H}_7(\mathbb{H})$ and investigate the maximal order of their holonomy group. First we show that $$ \mathrm{Aut}(\mathbb{R}^3 \tilde\times \mathbb{R}^4) \cong \mathrm{Hom}(\mathbb{R}^4, \mathbb{R}^3) \rtimes O(\mathbf{J};2,2),$$ where $O(\mathbf{J};2,2) = SO_0(2,2) \times \mathbb{R}^+$. Then we prove that there exists an almost Bieberbach group $\varPi \subset \mathcal{H}_7(\mathbb{H})\rtimes\mathrm{Aut}(\mathcal{H}_7(\mathbb{H}))$ whose maximal holonomy group has order $36$.

2010 Mathematics Subject Classification: 20H15, 20F18, 20E99, 53C29
Key Words and Phrases: almost Bieberbach group, holonomy group, infra-Nilmanifold

⋅ 28th-A-10:10 − 10:30 Group actions and localized mirror functors (Cheol-Hyun Cho)

조철현((서울대))
Cheol-Hyun Cho, Seoul National University

We explain localized mirror functors and its graded and equivariant versions with finite group action. A subtlety arise when we try to compare twisted complexes of geometric Fukaya categories and we discuss how to resolve the issue. This is based on joint works with Hansol Hong and Siu-Cheong Lau.

2010 Mathematics Subject Classification: 53D37
Key Words and Phrases: Fukaya category, mirror symmetry

⋅ 28th-B-10:40 − 11:00 On the classification of a large set of rational 3-tangle diagrams (Bo-hyun Kwon)

권보현((고려대))
Bo-hyun Kwon, Korea University

We note that a rational 3-tangle diagram is obtained from a combination of four generators. There is an algorithm to distinguish two rational 3-tangle diagrams up to isotopy. However, there is no perfect classification about rational 3-tangle diagrams such as the classification of rational 2-tangle diagrams corresponding to rational numbers. In this talk, we classify a large set of rational 3-tangles which are generated by only three generators.

2010 Mathematics Subject Classification: 57M27
Key Words and Phrases: rational 3-tangles, splitting condition, Dehn parameterization, standard parameterizaion

⋅ 28th-B-11:00 − 11:20 Upper bound of the lattice stick number of rational links with exactly 4 $z$-sticks (Hyoungjun Kim, Sungjong No)

김형준*((이화여대)), 노성종((이화여대))
Hyoungjun Kim*, Ewha Womans University, Sungjong No, Ewha Womans University

The lattice stick number $s_L(L)$ of a link $L$ is defined to be the minimal number of straight line segments required to construct a stick presentation of $L$ in the cubic lattice. In this paper, we find the upper bound of the lattice stick number of rational links with fraction $\frac{q}{p}$ by using exactly 4 $z$-sticks is $2(p+q)+5$.

2010 Mathematics Subject Classification: 57M25
Key Words and Phrases: knot, lattice stick

⋅ 28th-B-11:30 − 11:50 Upper bound on stick number of Montesinos link (Sungjong No, Seungsang Oh, Hwa Jeong Lee)

노성종*((이화여대)), 오승상((고려대)), 이화정((대구경북과학기술원))
Sungjong No*, Ewha Womans University, Seungsang Oh, Korea University, Hwa Jeong Lee, DGIST

Negami found an upper bound on the stick number $s(K)$ of a nontrivial knot $K$ in terms of the minimal crossing number $c(K)$, which is $s(K) \leq 2c(K)$. Huh, No and Oh proved that $s(L) \leq c(L)+2$ for all $2$-bridge knots and links $L$ with at least six crossings. Let $K$ be a knot or link which admits a reduced Montesinos diagram having $c(K)$ crossings. If each rational tangle of the diagram has five or more index of the related Conway notation, then $s(K)\leq c(K)+4$. In particular, if $K$ is alternating, then $s(K)\leq c(K)+1$.

2010 Mathematics Subject Classification: 57M25
Key Words and Phrases: knot, link, Montesinos, stick

⋅ 28th-B-11:50 − 12:10 The Brown-Peterson spectra (Dae-Woong Lee)

이대웅((전북대))
Dae-Woong Lee, Chonbuk National University

In this talk, we describe some fundamental results on the Brown-Peterson spectra and the local cohomology spectral sequences. In particular, we give an explicit description of the behaviour of the local cohomology spectral sequence for the Brown-Peterson spectra graded over the representation ring, and explore the homotopy structure of the Real-oriented Brown-Peterson spectrum. We also examine the local cohomology structures of the basic block and the negative block of the homotopy of BPR$\langle 3\rangle$, and their Anderson duals. This is a part of a joint work with J. P. C. Greenlees.

2010 Mathematics Subject Classification: 55P42, 55P43, 13D45, 55P91, 55T99, 55U30, 13H10
Key Words and Phrases: Brown-Peterson spectrum, real orientation, Anderson duality, equivariant cohomology, Gorenstein duality, local cohomology spectral sequence

⋅ 28th-C-14:10 − 14:30 Staructurally stability of transitive sets (Manseob Lee, Junmi Park)

이만섭((목원대)), 박준미*((충남대))
Manseob Lee, Mokwon University, Junmi Park*, Chungnam National University

Let $f$ be a diffeomorphism on a compact smooth Riemannian manifold $M$ endowed with the $C^1$ topology, and let $\Lambda$ be a chain transitive set for $f$. Then we can defined the ``local structurally stability" on $\Lambda.$ In this talk, we show that if $f$ is structurally stable on a chain transitive set $\Lambda$, then $\Lambda$ is hyperbolic. Moreover, it does satisfy for a transitive set also.

2010 Mathematics Subject Classification: 37C20, 37D20
Key Words and Phrases: structurally stable, hyperbolic, transitive, chain transitive

⋅ 28th-C-14:30 − 14:50 On the strong average shadowing property and dominated splitting of flows (Bowon Kang, Namjip Koo, Manseob Lee)

강보원*((충남대)), 구남집((충남대)), 이만섭((목원대))
Bowon Kang*, Chungnam National University, Namjip Koo, Chungnam National University, Manseob Lee, Mokwon University

The average shadowing property (ASP) introduced by Blank. Sakai proved that on a closed $C^1$ surface, the $C^1$ interior of the set of all $C^1$ diffeomorphisms with the average shadowing property is characterized by the set of Anosov diffeomorphisms. Also, Arbieto and Ribeiro extended the results of Sakai for flows and showed that the interior of the set of flows with the average shadowing property on a three-dimensional closed manifold is formed by transitive Anosov flows. In this talk, we will investigate the relationship between ASP and dominated splitting in flows n-dimensional closed manifolds.

2010 Mathematics Subject Classification: 37C10, 37D30
Key Words and Phrases: average shadowing property, flow, dominated splitting
Probability and Statistics

⋅ 28th-B-10:40 − 11:00 Inequalities for positive module operators on von Neumann algebras (Byoung Jin Choi, Un Cig Ji, Yongdo Lim)

최병진*((충북대)), 지운식((충북대)), 임용도((성균관대))
Byoung Jin Choi*, Chungbuk National University, Un Cig Ji, Chungbuk National University, Yongdo Lim, Sungkyunkwan University

In this talk, we establish the Cauchy-Schwarz and Golden-Thompson inequalities for module operators, a generalization of a (noncommutative) conditional expectation, on a von Neumann algebra. We also apply these inequalities to the Bennett inequality and a uncertainty relation, a generalization of the Schr\"{o}dinger uncertainty relation, for conditional expectations.

2010 Mathematics Subject Classification: 46L53, 47A63, 81P45
Key Words and Phrases: module operator, conditional expectation, Golden-Thompson inequality, Bennett inequality, Schr\"{o}dinger uncertainty relation

⋅ 28th-B-11:00 − 11:20 Macroscopic fractal random sets (Kunwoo Kim)

김건우((포항공대))
Kunwoo Kim, POSTECH

In this talk, we first introduce macroscopic fractal dimensions introduced by Barlow and Taylor (1992), and then consider various random sets and their macroscopic fractal dimensions. In particular, we provide some formula for the macroscopic Hausdorff/Minkowski dimensions of the range of a general random walk on $\mathbb{Z}^d$. This is based on join work with N. Georgiou, D. Khoshnevisan and A. Ramos.

2010 Mathematics Subject Classification: 60G50
Key Words and Phrases: Macroscopic Hausdorff/Minkowski dimensions, random walks

⋅ 28th-B-11:30 − 11:50 Ruin probabilities of multivariate risk models with common shock dependence and regime switching (Jerim Kim, Hyung-Tae Ha)

김제림*((서울시립대)), 하형태((가천대))
Jerim Kim*, University of Seoul, Hyung-Tae Ha, Gachon University

We extend that the continuous-time risk model with the thinning dependence structure for the common Poisson stream of accidents addresses the time-varying behavior of accidents occurrences by exploiting a flexible Poisson process of the Markov-modulated Poisson process (MMPP). We derive the ultimate and finite time ruin probability of the correlated risk model under stochastic environments in this paper. We investigate strategic allocations for the initial surplus of the individual risk process.

2010 Mathematics Subject Classification: 60J28
Key Words and Phrases: risk model, surplus process, ruin probability, first passage time

⋅ 28th-B-11:50 − 12:10 Gated polling systems with large switchover times (Bara Kim, Jeongsim Kim)

김바라*((고려대)), 김정심((충북대))
Bara Kim*, Korea University, Jeongsim Kim, Chungbuk National University

We consider a sequence of cyclic polling systems, indexed by $k$. The switchover time distributions depend on $k$, but the interarrival time and service time distributions are independent of $k$. The service discipline at all queues is gated. We investigate the limits of the moments of the scaled queue length distribution, when the switchover times go to infinity. Using the distributional form of Little's law, we obtain the limits of the moments of the scaled sojourn time distribution, when the switchover times go to infinity.

2010 Mathematics Subject Classification: 60K25
Key Words and Phrases: polling system, asymptotic analysis, distributional Little's law
Applied Mathematics

⋅ 28th-A-09:40 − 09:45 {\scriptsize \rm [Contributed Talk(5min)+Poster Session(30min)]} Asymptotic behavior of solutions for a quasilinear parabolic equation with time-dependent coefficient source (Rui Yang)

양예((부산대))
Rui Yang, Pusan National University

A quasilinear parabolic equation with time-dependent coefficient source under Dirichlet boundary condition is studied in this paper. By the technique of differential inequalities, the conditions on the nonlinearities to guarantee that $u(x, t)$ exists globally or blows up at some finite time are established, respectively. Finally, upper and lower bounds of the blow-up time when blow-up does occur are derived.

2010 Mathematics Subject Classification: 34B16, 34B18, 35B40
Key Words and Phrases: quasilinear parabolic, time-dependent, blow-up, lower bound, upper bound

⋅ 28th-C-14:10 − 14:30 Shallow arches with a strong damping term (Jun Hong Ha)

하준홍(( 한국기술교육대))
Jun Hong Ha, Korea University of Technology and Education

Building long span arch roofs and bridges has been an important practical problem that has occupied structural engineers for many years. The motion of such structures has been studied by engineers and mathematicians since at least 1930s. General mathematical models for the motion of arches and membrane like structures has been studied after 1970s, and an interesting one of them is given by the following non-local integro-differential equation \[ y_{tt}+\alpha\Delta^2 y -\left(\beta+\gamma\int_\Omega|\nabla y|^2\, dx \right) \Delta y +\kappa y_t+\mu\Delta^2 y_t =f. \leqno(1) \] The function $y=y(x,t)$ describing the membrane's deflection is defined on $\Omega \times (0,T)$, where $\Omega\in {\mathbf R}^d$. In the one-dimensional case $d=1$, function $y(x,t)$ describes the deflection of an arch, which is positioned over the interval $\Omega=(0,l)$ of the $x$ axis. This presentation talks about a rigorous mathematical framework for the behavior of arch and membrane like structures. Our main goal is to incorporate moving point loads $f=f(x,t)$, for an example $f=Q \delta(x-ct)$. The existence and uniqueness of weak solutions of (1) are proved, and the convergence is discussed when $\mu \to 0$. The theory is applied to a car moving on a bridge.

2010 Mathematics Subject Classification: 35L75
Key Words and Phrases: shallow arches, damping, Cahuchy problem

⋅ 28th-C-14:30 − 14:50 Performance of ensemble-based filters for an idealized ocean thermohaline circulation model (Sangil Kim, Il-Hyo Jung)

김상일*((한국외대)), 정일효((부산대))
Sangil Kim*, Hankuk University of Foreign Studies, Il-Hyo Jung, Pusan National University

The sequential filtering scheme provides a suitable framework for estimating and tracking geophysical states of systems as new data become available on line. Mathematical foundations of sequential Bayesian filtering are reviewed with emphasis on practical issues for both particle filters and Kalman-based filters. In this study, the sequential Importance resampling method (SIR), Ensemble Kalman Filter (EnKF), and the Maximum Entropy Filter (MEF) are tested in a relatively high dimensional ocean model that conceptually represents the Atlantic thermohaline circulation. The model exhibits large-amplitude transitions between strong (thermo-dominated) and weak (salinity-dominated) circulations that represent climate states between ice-age and normal climate. The performance of the particle-based schemes is compared with the convergent results from SIR based on measurement errors, observation locations, and particle sizes in various sets of twin experiments. The sensitivity analysis shows strength and weakness of each filtering method when applied to multimodal non-linear systems. As the number of particles is increased, SIR achieves the convergent results that are mathematically optimal solutions. EnKF shows suboptimal results regardless of sample sizes, and MEF achieves the optimal solution even with a small sample size. Both EnKF, and MEF produces robust results with a relatively small sample size or increased measurement locations. Small measurement errors or short intervals of observations (or, more frequent observations) significantly improve the performances of SIR and EnKF, and MEF still show robust results even with a relatively small sample size or sparse measurement locations when the system experiences the transition between one region to the other region.

2010 Mathematics Subject Classification: 35R30
Key Words and Phrases: ocean state estimation, sequential Monte Carlo methods, sequential importance resampling, ensemble Kalman filter, maximum entropy filter

⋅ 28th-C-14:50− 15:10 The fractional Fourier transform and its applications to sampling theory (Sinuk Kang)

강신욱((원광대))
Sinuk Kang, Wonkwang University

As a generalization of the Fourier transform, the fractional Fourier transform (FrFT) plays an important role both in theory and in application of signal processing. We introduce FrFT and discuss its useful mathematical properties. And then we present certain applications benefited from FrFT including sampling theorem associated with FrFT domain.

2010 Mathematics Subject Classification: 94A20
Key Words and Phrases: the fractional Fourier transform, sampling theory
Mathematical Education

⋅ 28th-A-09:00 − 09:20 한국과학영재학교 수학교육모델(Mathematics education model for Korea Science Academy) (Hun Kim)

김훈((한국과학영재학교))
Hun Kim, Korea Science Academy of KAIST

본 연구에서는 한국 최초의 과학영재학교로써 지난 15년 동안 수행해 왔던 수학 교육활동을 분석하고자 한다. 이를 통해서 구성원들이 공유할 수 있는 교육모델을 제시하고자 한다. 이를 위해 카이스트 부설화 이후 수리정보과학부에서 수행한 교육 활동 분석하고 교육 모델에 따른 교육활동 분류하고자 한다. 이 결과는 한국과학영재학교 교육과정 개정 자료로 활용할 뿐만 아니라 타 과학영재학교의 참고자료로 활용될 수 있을 것이다.

2010 Mathematics Subject Classification: 97B40
Key Words and Phrases: 수학영재교육

⋅ 28th-A-09:20 − 09:40 학생중심교수법 적용사례: 선형대수학을 중심으로 (Sang-Gu Lee, Jae Hwa Lee)

이상구((성균관대)), 이재화*((성균관대))
Sang-Gu Lee, Sungkyunkwan University, Jae Hwa Lee*, Sungkyunkwan University

본 발표에서는 2017학년도 1학기 S대학교의 학생중심교수법 개발지원사업의 일환으로 개발된 선형대수학 강의에 관하여 보고한다. 본 강의는 선형대수학 이론 강의와 더불어 학습한 내용을 계산과 시뮬레이션을 통해 실습하고 그 과정을 보고서로 제출하고 발표하는 등 학생들이 학습 전과정에 참여하도록 유도한다. 이를 위해 본 연구진은 다양한 웹 링크와 시뮬레이션 및 계산이 가능한 코드를 갖춘 실습실을 개발하여 강의에 활용, 학생들이 언제든지 실습할 수 있게 하였고, 계산된 결과를 LMS를 통해 동료 및 교수자와 함께 질문, 답변, 토론하며 개념에 대해 깊게 이해하고 설명할 수 있도록 하였다. 또한 이 과정을 평가에 적절히 반영하여 학생들은 학습하는 과정에서 자신의 문제를 해결해가는 과정을 서술하고, 발표하는 비판적 사고 능력을 자연스럽게 갖추도록 힘썼다. 본 연구진이 제안하는 대학 수학 강좌의 운영 방식은 미적분학, 공학수학, 미분방정식, 기초통계학 등 다른 수학 강좌를 운영하는 모델로 활용될 수 있다. 전체내용은 웹사이트 http://matrix.skku.ac.kr/2017-LA-portfolio-sglee/에서 확인할 수 있다.

2010 Mathematics Subject Classification: 97U20, 97U70
Key Words and Phrases: 디지털 시대, 수학, 인터넷, 선형대수학, 대학수학교육, 학생중심교수법

⋅ 28th-A-09:50 − 10:10 문항구성요소에 따른 과정중심평가 문항 개발 방안 (Bo Euk Suh)

서보억((충남대))
Bo Euk Suh, Chungnam National University

현재2015개정 수학과 교육과정의 현장 적용을 앞두고 평가에 대한 높은 관심을 보이고 있다. 특히 이번 교육과정에서는 학교현장에서 과정중심평가를 새로운 평가의 대안으로 제시하고 있다. 과중중심평가는 수업과 평가가 동시에 이루어지는 평가의 체제로 기존의 수행평가보다 수업중심적평가 체제이다. 특히 자유학기제 등 학생들의 다양한 교육활동이 강조되는 시점에서 과정중심평가는 새로운 대안으로 제시되고 있다. 과정중심평가를 성공적으로 정착하기 위해서는 어떤 내용을 어떤 문항으로 평가할 것인가가가장 중요한 문제이다. 수학교육에서 내용은 어느 정도는 결정되어져 있기 때문에 교사의 관심은 어떤 문항으로 평가할 것인가이다. 평가문항을 어떻게 구성하는 것이 과정중심평가와 부합되는가에 대한 심각한 고민이 필요하다. 기본적으로 수학과의 과정중심평가는 수업의 내용과 결부되고, 개념, 원리, 법칙의 이해의 과정 및 기능을 습득하는 과정에서 발생하는 수학적 과정이 중심이 되어야 한다. 이러한 과정은 교사의 수업방과 재구조화에 의해 어느 정도 해결될 수 있을 것이다. 본 연구에서는 문항이 가지는 네 가지 요소에 초점을 두었다. 주어진 것, 배경지식, 해결과정, 구할 것이 그것이다. 이러한 네 가지 하위요소를 각각 $A(x)$, $B(y)$, $C(z)$, $D(w)$라고 하고, 각각의 요소가 존재하는냐 하지 않느냐에 따라 문항의 유형을 16가지로 구분하였다. 예를 들어, 네 가지 요소가 모두 있는 유형을 $ABCD$, 네가지 요소가 모두 없는 유형을 $xyzw$라고 부를 것이다. 이를 기반으로 본 연구에서는 과정중심평가 문항의 개발 방안을 제시하였다.

2010 Mathematics Subject Classification: 97B50
Key Words and Phrases: 수학평가문항, 과정중심평가, 문항의 구성요소

⋅ 28th-A-10:10 − 10:30 Self learning materials of Galois theory for teachers (Hyunyong Shin)

신현용((한국교원대))
Hyunyong Shin, Korea National University of Education

We propose a self learning materials of Galois theory for mathematics teachers. We give complete solutions of cubic and quartic polynomials to help understanding Galois theory.

2010 Mathematics Subject Classification: 97U99
Key Words and Phrases: self Learning, Galois theory

⋅ 28th-B-10:40 − 11:00 창의성 함양을 위한 중학교 수학 프로그램 개발의 방향 (Joonkook Shin, Jeongja Kim)

신준국*((충남대)), 김정자((대전탄방중))
Joonkook Shin*, Chungnam National University, Jeongja Kim, Daejeon Tanbang Middle School

최근의 수학과 교육과정을 보면, 창의성을 강조하고 있다. 수학교과에서는 ‘수학적 창의성’이라는 표현을 사용하여 미래 사회를 살아가는 데 중요한 사고의 특성으로 인식하고 있으며, 수학적 과제를 해결하는 과정에서 다양하고 독창적인 해결방법을 산출하거나 새로운 관점에서 과제를 탐구하고 지식을 구성하는 능력으로 규정하고 있다. 우리나라의 경우 1995년 ‘5·31 교육개혁방안’에서 처음 창의교육의 중요성을 강조하였으며, 2009개정 수학과 교육과정에서는 창의성을 교수·학습에서 교사가 고려해야하는 수업방법 중 하나로 제시하였고, 2015개정 수학과 교육과정에서는 수학과의 6개 교과역량 중 ‘창의성’ 역량을 제시하고 있다. 특히 2018년부터 본격 시행에 들어가는 2015개정 교육과정에서는 ‘창의·융합형 인재’ 양성을 핵심 목표로 설정하였는데, 이는 창의성을 바탕으로 창의·융합적 인간 양성을 학교 교육의 핵심과제로 부각시킨 것이다. 이러한 창의성 교육에 대한 강조에도 불구하고 사회적 공감과 현장 교사의 수업 역량 등은 충분하지 않다. 따라서 수학교실에서 창의성 함양에 부합된 교수학습 자료의 개발은 절대적으로 요구되는데 여기서는 수학교실에서 창의성 함양을 위한 새로운 교수학습 자료에 대한 개발 방향과 구체적인 사례를 살펴보고자 한다.

2010 Mathematics Subject Classification: 97Mxx
Key Words and Phrases: 창의성, 창의·융합형 인재, 교수학습 자료

⋅ 28th-B-11:00 − 11:20 Geometric tube design of the single Archimedes star dome (Hong Taek Hwang, Gyungsoo Woo, Won Suk Yoo)

황홍택*((금오공대)), 우경수((금오공대)), 유원석((금오공대))
Hong Taek Hwang*, Kumoh National Institute of Technology, Gyungsoo Woo, Kumoh National Instute of Technology, Won Suk Yoo, Kumoh National Instute of Technology

The soccer ball ``Telstar" is one of realities of the three dimensional sphere shape. For a given RPS (regular pentagonal shape), it is possible for us to image a general reality of sphere shape by applying the Telstar formation scheme to the given RPS. Eventually, through a series of geometric tube design experiments, we can establish this general reality of sphere shape. We call this reality the Archimedean star with respect to the given RPS. There are three kinds of Archimedean star such as horizontal star, skewed star and vertical star on geometric tube design. We established a natural combination of a single Archimedean horizontal star and the single Archimedean vertical star. Moreover, we get a dome modification derived from this natural combination of two single Archimedean stars mentioned above.

2010 Mathematics Subject Classification: 97U99
Key Words and Phrases: geometric tube design, Archimedean star

⋅ 28th-B-11:30 − 11:35 {\scriptsize \rm [Contributed Talk(5min)+Poster Session(30min)]} The development of students' proof construction in undergraduate mathematics education (Kyungwon Lee, Oh Nam Kwon)

이경원*((서울대)), 권오남((서울대))
Kyungwon Lee*, Seoul National University, Oh Nam Kwon, Seoul National University

Proof learning in undergraduate mathematics course plays a role for dealing with the mathematical content and interacting in the mathematics classroom. Many researches on teaching and learning of proof focused on proof construction, proof for reasoning, and understanding a proof from classroom based approach. Although we may expect that proof production in students' individual learning and group discussion about proof have a strong relationship, it's hard to be supported by the results of prior research about proof learning. We will explore the development of students' proof by analyzing the interrelationship between proofs constructed by students and discourse in classroom.

2010 Mathematics Subject Classification: 97
Key Words and Phrases: proof construction, group discussion, undergraduate mathematics education

⋅ 28th-B-11:35 − 11:40 {\scriptsize \rm [Contributed Talk(5min)+Poster Session(30min)]} Undergraduate students’ beliefs about mathematical proofs (Yaerin Oh, Oh Nam Kwon)

오예린*((서울대)), 권오남((서울대))
Yaerin Oh*, Seoul National University, Oh Nam Kwon, Seoul National University

It has been reported that undergraduate students have difficulties in learning mathematical proofs. There have been various efforts to support undergraduates' learning of mathematical proofs. Mostly, researchers focused on students’ proof production. To understand undergraduates’ proof learning in depth, it is necessary to understand their beliefs about mathematical proofs. In this study, we explore undergraduate students’ beliefs on mathematical proofs and look for implication in proof education.

2010 Mathematics Subject Classification: 97C30
Key Words and Phrases: beliefs, proof learning, undergraduate mathematics education

⋅ 28th-B-11:40 − 12:00 The analyse of the map of Myocheong's west capital of old Korea by topological method and geometrical method (Q-Heung Choi, Tacksun Jung)

최규흥*((인하대)), 정택선((군산대))
Q-Heung Choi*, Inha University, Tacksun Jung, Kunsan National University

We analyse the map of Myocheong's west capital of old Korea (AD 1135) by topological method and geometrical method and compare it with the map of North Korea Pyongyang.

2010 Mathematics Subject Classification: 51K99, 54B30
Key Words and Phrases: Myocheong's west capital, topological method
Discrete Mathematics

⋅ 28th-A-09:00 − 09:20 A sufficient condition for DP-4-colorability (Seog-Jin Kim, Kenta Ozeki)

김석진*((건국대)), 켄타 오제키((Yokohama National University))
Seog-Jin Kim*, Konkuk University, Kenta Ozeki, Yokohama National University

DP-coloring of a simple graph is a generalization of list coloring, and also a generalization of signed coloring of signed graphs. It is known that for each $k \in \{3, 4, 5, 6\}$, every planar graph without $C_k$ is 4-choosable. Furthermore, Jin, Kang, and Steffen (2016) showed that for each $k \in \{3, 4, 5, 6\}$, every signed planar graph without $C_k$ is signed 4-choosable. In this paper, we show that for each $k \in \{3, 4, 5, 6\}$, every planar graph without $C_k$ is 4-DP-colorable, which is an extension of the above results. This is joint work with Kenta Ozeki.

2010 Mathematics Subject Classification: 05C15
Key Words and Phrases: list coloring, signed graph, DP-coloring

⋅ 28th-A-09:20 − 09:40 Variants of Woodall's conjecture (Maria Chudnovsky, Katherine Edwards, Rin Gi Kim, Alex Scott, Paul Seymour)

Maria Chudnovsky((Princeton University)), Katherine Edwards((Princeton University)), 김린기*((한국과학기술원)), Alex Scott((Oxford University)), Paul Seymour((Princeton University))
Maria Chudnovsky, Princeton University, Katherine Edwards, Princeton University, Rin Gi Kim*, KAIST, Alex Scott, Oxford University, Paul Seymour, Princeton University

A dijoin in a digraph is a set of edges meeting every directed cut. D. R. Woodall conjectured in 1976 that if $G$ is a digraph, and every directed cut of $G$ has at least $k$ edges, then there are $k$ pairwise disjoint dijoins. This is proved for $k\le 2$, but it is still open for $k=3$. In this talk, we discuss variants of Woodall's conjecture.

2010 Mathematics Subject Classification: 05C20
Key Words and Phrases: dijoin, directed cut

⋅ 28th-A-09:50 − 10:10 On 2-walk-regular graphs (Jongyook Park)

박종육((원광대))
Jongyook Park, Wonkwang University

A $t$-walk-regular graph is a common generalization of distance-regular graphs on the one hand and $t$-arc-transitive graphs on the other hand. We focus on the case where $t =2$ because $s$-walk-regular graphs are $t$-walk-regular if $s\geq t$ and many properties of distance-regular graphs can be generalized to $2$-walk-regular graphs. In this talk, we first introduce some known results that hold for $2$-walk-regular graphs but are not true in general for $1$-walk-regular graphs. And then we will generalize a known result of distance-regular graphs to the class of 2-walk-regular graphs.

2010 Mathematics Subject Classification: 05E30, 05C50
Key Words and Phrases: distance-regular graphs, $t$-walk-regular graphs

⋅ 28th-A-10:10 − 10:30 Minimum Lee weights of cyclic self-dual codes over Galois rings (Boran Kim, Yoonjin Lee)

김보란*((이화여대 수리과학연구소)), 이윤진((이화여대))
Boran Kim*, Institute of Mathematical Sciences, Ewha Womans University, Yoonjin Lee, Ewha Womans University

We completely determine the minimum Lee weights of cyclic self-dual codes over a Galois ring $GR(p^2,m)$ of length $p^k$, where $m$ and $k$ are positive integers and $p$ is a prime number. We obtain all cyclic self-dual codes over $GR(2^2,1)\cong \mathbb Z_4$ of lengths $16$ and 32 with their Lee weight enumerators. We also find cyclic self-dual codes over $GR(3^2,1) \cong \mathbb Z_9$ (respectively, $GR(3^2,2)$) of lengths up to $27$ (respectively, $9$). Most of the cyclic self-dual codes we found are extremal with respect to the Lee weights.

2010 Mathematics Subject Classification: 94B15
Key Words and Phrases: cyclic codes, self-dual codes, Galois rings, minimum Lee weights

⋅ 28th-C-14:10 − 14:25 The $m$-step competition graphs of $d$-partial orders (Jihoon Choi)

최지훈((서울대))
Jihoon Choi, Seoul National University

Let $D$ be a digraph and $m$ be a positive integer. A vertex $y$ is called an \emph{$m$-step prey} of a vertex $x$ in $D$ if there exists a directed walk from $x$ to $y$ of length $m$. The \emph{$m$-step competition graph} of $D$, denoted by $C^m(D)$, is defined to be the simple graph having the same vertex set as $D$ and having an edge $xy$ if and only if there exists an $m$-step common prey of $x$ and $y$ in $D$. For a positive integer $d$, a digraph $D$ is called a \emph{$d$-partial order} if $V(D) \subset \mathbb{R}^d$ and there is an arc from a vertex $\mathbf{x}$ to a vertex $\mathbf{y}$ if and only if $\mathbf{x}$ is componentwise greater than $\mathbf{y}$. In this talk, we study the $m$-step competition graphs of $d$-partial orders and reveal a relation to the competition graphs of $d$-partial orders. Especially, we define the notion of partial order $m$-step competition dimension of a graph $G$ and show that how it behaves as $m$ varies.

2010 Mathematics Subject Classification: 05C20
Key Words and Phrases: competition graph, $m$-step competition graph, $d$-partial order

⋅ 28th-C-14:25 − 14:40 On Riordan graphs (Ji-Hwan Jung, Gi-Sang Cheon, Seyed Ahmad Mojallal, Sergey Kitaev)

정지환*((성균관대)), 천기상((성균관대)), Seyed Ahmad Mojallal((성균관대)), Sergey Kitaev((University of Strathclyde))
Ji-Hwan Jung*, Sungkyunkwan University, Gi-Sang Cheon, Sungkyunkwan University, Seyed Ahmad Mojallal, Sungkyunkwan University, Sergey Kitaev, University of Strathclyde

In this talk, we use the theory of Riordan matrices to introduce the notion of a Riordan graph. The Riordan graphs are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other families of graphs. The Riordan graphs are proved to have a number of interesting (fractal) properties, which can be useful in creating computer networks with certain desired features, or in obtaining useful information when designing algorithms to compute values of graph invariants. The main focus in this paper is the study of structural properties of families of Riordan graphs obtained from infinite Riordan graphs, which includes a fundamental decomposition theorem and the generalization of some known results for the Pascal graphs.

2010 Mathematics Subject Classification: 05Cxx, 05A15
Key Words and Phrases: Riordan matrix, Riordan graph, Pascal graph, Toeplitz graph, fractal

⋅ 28th-C-14:40 − 14:55 Domino tiling for augmented Aztec rectangles and their chains (Hyung Gi Kim, Sangyop Lee, Seungsang Oh)

김형기*((고려대)), 이상엽((중앙대)), 오승상((고려대))
Hyung Gi Kim*, Korea University, Sangyop Lee, Chung-Ang University, Seungsang Oh, Korea University

We have made great progress in the study of domino tilings (or perfect matchings) of the augmented Aztec diamond and its variants. In this talk, we consider augmented Aztec rectangles, and vertical and horizontal chains of augmented Aztec rectangles. I will introduce the bijective relation between domino tilings for these regions and the well-known Delannoy paths, and the exact numbers of domino tilings for these regions using these bijection.

2010 Mathematics Subject Classification: 05A15, 05B45, 05C70
Key Words and Phrases: Aztec diamond, augmented Aztec rectangle, domino tiling, perfect matching

⋅ 28th-C-14:55 − 15:10 Constructions of formally self-dual codes over $\mathbb{Z}_4$ and their weight enumerators (Yoonjin Lee, Jinjoo Yoo)

이윤진((이화여대)), 유진주*((이화여대))
Yoonjin Lee, Ewha Womans University, Jinjoo Yoo*, Ewha Womans University

We characterize relations between Lee weight enumerators of formally self-dual codes over $\mathbb{Z}_4$ of length $n$ and those of length $n+2$. Based on these relations, we find explicit methods for constructing formally self-dual codes over $\mathbb{Z}_4$. Using these methods, we find 46 inequivalent formally self-dual codes whose minimum Lee weights are larger than self-dual codes of the same length. Also, we obtain 19 non-linear extremal binary formally self-dual codes of lengths 12, 16, and 20, up to equivalence, from formally self-dual codes over $\mathbb{Z}_4$ by using the Gray map.

2010 Mathematics Subject Classification: 94B05, 11T71
Key Words and Phrases: formally self-dual code, Lee weight enumerator, Gray map
Cryptography

⋅ 28th-B-11:00 − 11:20 A two-round protocol for multi-party key agreement (Soyoung Ahn, Taewan Kim, Hyang-Sook Lee, Seongan Lim)

안소영*((이화여대)), 김태완((한국전자통신연구원)), 이향숙((이화여대)), 임선간((이화여대, 수리과학연구소))
Soyoung Ahn*, Ewha Womans University, Taewan Kim, Electronics and Telecommunications Research Institute, Hyang-Sook Lee, Ewha Womans University, Seongan Lim, Institute of Mathematical Sciences, Ewha Womans University

In this talk, we present a lattice based two-round multi-party key agreement protocol. Our construction is based on the threshold multi-key fully homomorphic encryption scheme (MW-TMFHE) which was proposed by Mukeherjee and Wichs in Eurocrypt 2016. We note that only the additive homomorphic part of the MW-TMFHE scheme is used for our multi-party key agreement protocol and it simplifies the related parameters of the MW-TMFHE scheme.

2010 Mathematics Subject Classification: 94A60
Key Words and Phrases: LWE problem, treshold multi-key fully homomorphic encryption, multi-party key agreement

⋅ 28th-B-11:30 − 11:50 About cryptanalysis of indistinguishability obfuscator (Minki Hhan, Jung Hee Cheon, Changmin Lee)

한민기*((서울대)), 천정희((서울대)), 이창민((서울대))
Minki Hhan*, Seoul National University, Jung Hee Cheon, Seoul National University, Changmin Lee, Seoul National University

Recently indistinguishability obfuscation (iO) arises as a ``dream of programming", which makes completely secure program with respect to reverse engineering and gives many other useful cryptographic tools. In this talk, we briefly introduce what is iO and its recent analyses.

2010 Mathematics Subject Classification: 11T71, 94A60
Key Words and Phrases: indistinguishability obfuscation, cryptographic multilinear map

⋅ 28th-B-11:50 − 12:10 The UOV attack on the simple vector signature scheme (Cheol Min Park, Kyung-Ah Shim, Namhun Koo)

박철민*((국가수리과학연구소)), 심경아((국가수리과학연구소)), 구남훈((성균관대))
Cheol Min Park*, National Institute for Mathematical Sciences, Kyung-Ah Shim, National Institute for Mathematical Sciences, Namhun Koo, Sungkyunkwan University

In this talk, we present an efficient attack on the Simple Vector Signature Scheme with Vinegar (SVSv). We breaks the SVSv cryptosystem by UOV attack and solving a system of multivariate quadratic equations using the F$_4$ algorithm. From a practical point of view, we are able to break their parameter at 128-bit security level in 3 seconds.

2010 Mathematics Subject Classification: 14G50
Key Words and Phrases: post-quantum cryptography, UOV attack, multivariate-quadratic scheme, Gr\"obner basis

⋅ 28th-C-14:10 − 14:30 Cryptanalysis of CSSv and SVSv signature scheme in ICISC 2016 (Kyung-Ah Shim, Cheol-Min Park, Namhun Koo)

심경아((국가수리과학연구소)), 박철민((국가수리과학연구소)), 구남훈*((성균관대))
Kyung-Ah Shim, National Institute for Mathematical Sciences, Cheol-Min Park, National Institute for Mathematical Sciences, Namhun Koo*, Sungkyunkwan University

In ICISC 2016, Duong et al. proposed CSSv signature scheme, a revisited version of CUOV (Cubic UOV) to prevent the attack of Hashimoto from being applied, and SVSv signature scheme to modify CSSv scheme to a multivariate quadratic signature scheme. Soon afterwards they found that SVSv scheme is not secure against HighRank attack, and proposed a revised version of the scheme. By the way, in PKC 2015, Faugere et al. introduced a key recovery attack on the MQQ-SIG, a multivariate signature scheme based on multivariate quadratic quasigroup. In this talk, we show that the idea of Faugere is also applicable on CSSv and revised SVSv scheme, and hence their schemes are totally broken.

2010 Mathematics Subject Classification: 14G50
Key Words and Phrases: key recovery attack, cryptanalysis, CSSv signature scheme, SVSv signature scheme

⋅ 28th-C-14:30 − 14:50 Lizard: Cut off the tail! The practical post-quantum public-key encryption from LWE and LWR (Jung Hee Cheon, Duhyeong Kim, Joohee Lee, Yongsoo Song)

천정희((서울대)), 김두형*((서울대)), 이주희((서울대)), 송용수((서울대))
Jung Hee Cheon, Seoul National University, Duhyeong Kim*, Seoul National University, Joohee Lee, Seoul National University, Yongsoo Song, Seoul National University

The LWE problem has been widely used in many constructions for post-quantum cryptography due to its strong security reduction from the worst-case of lattice hard problems and its lightweight operations. The Public Key Encryption (PKE) schemes based on the LWE problem have a simple and fast decryption, but the encryption phase is rather slow due to large parameter size for the leftover hash lemma or Gaussian samplings. In this paper, we propose a novel PKE scheme, called Lizard, without relying on either of them. The encryption procedure of Lizard first combines several LWE samples as in the previous LWE-based PKEs, but the following step to re-randomize this combination before adding a plaintext is different: it removes several least significant bits of each component of the computed vector rather than adding an auxiliary error vector. Lizard is IND-CPA secure under the hardness assumptions of the LWE and LWR problems, and its variants achieve IND-CCA security in the (quantum) random oracle model. Our approach accelerates encryption speed to a large extent and also reduces the size of ciphertexts, and Lizard is very competitive for applications requiring fast encryption and decryption phases. Our IND-CCA secure PKE scheme, namely CCALizard, shows outstanding performance with concrete security: In our single-core implementation on an Intel Xeon E5-2620 CPU running at 2.10GHz, the encryption and decryption of CCALizard with $256$-bit plaintext space under 128-bit quantum security take only $40,345$ and $55,236$ cycles which are mean value for $100,000$ measurements. To achieve these results, we further take some advantages of sparse small secrets. Our Lizard will be submitted to the National Institute of Standards and Technology (NIST) call for post-quantum standard.

2010 Mathematics Subject Classification: 11T71, 94A60
Key Words and Phrases: post-quantum cryptography, public-key encryption, learning with rounding, learning with errors

⋅ 28th-C-14:50 − 15:10 Tweakable block ciphers secure beyond the birthday bound in the ideal cipher model (ByeongHak Lee, Jooyoung Lee)

이병학*((한국과학기술원)), 이주영((한국과학기술원))
ByeongHak Lee *, KAIST, Jooyoung Lee, KAIST

We propose new constructions of tweakable block ciphers from standard block ciphers. We begin with a simple construction, dubbed XHX, which makes a single call to the underlying block cipher using tweak-dependent keys. Viewed as a generalization of XEX, XTX and XPX, its security is proved up to $2^{(n+m)/2}$ queries in the ideal cipher model, when the block cipher operates on n-bit blocks using m-bit keys. Our main contribution is to prove the security of the cascade of two independent XHX constructions up to $\min\{2^{2(n+m)/3},2^{n+m/2}\}$ queries (ignoring logarithmic factors). The 2-round XHX is the first tweakable block cipher that achieves beyond-birthday-bound security with respect to the input size of the underlying block cipher in the ideal cipher model.

2010 Mathematics Subject Classification: 94A60
Key Words and Phrases: tweakable block cipher, beyond-the-birthday bound, ideal cipher model

CMAC

⋅ 28th-A-09:00 − 09:20 A study of accelerating the alternating direction method of multipliers (Hi Jun Choe, Hayeong Koh, Jongeun Kim)

최희준((연세대)), 고하영*((연세대)), 김종은((연세대))
Hi Jun Choe, Yonsei University, Hayeong Koh*, Yonsei University, Jongeun Kim, Yonsei University

The alternating direction methods are used commonly in various field. Especially, we discussed accelerating the methods for the case of minimizing the convex functions: $\min f(x)+g(y)$ subject to $Ax+By=c$.

2010 Mathematics Subject Classification: 80M50
Key Words and Phrases: convex optimization, ADMM

⋅ 28th-A-09:20 − 09:40 Curse of dimensionality in pricing multi-asset options (Jeonggyu Huh, Jaegi Jeon, Jeong-Hoon Kim, Hyejin Park)

허정규*((연세대)), 전재기((연세대)), 김정훈((연세대)), 박혜진((한양대))
Jeonggyu Huh*, Yonsei University, Jaegi Jeon, Yonsei University, Jeong-Hoon Kim, Yonsei University, Hyejin Park, Hanyang University

The number of tailor-made hybrid structured products has risen more prominently to fit each investor’s preferences and requirements as they become more diversified. The structured products entail synthetic derivatives such as combinations of bonds and/or stocks conditional on backing by underlying securities, stochastic volatility, stochastic interest rates or exchanges rates. The complexity of these multi-asset structures yields lots of difficulties of pricing the products. Because of the complexity, Monte-Carlo simulation is a possible choice to price them but it may not produce stable Greeks leading to a trouble in hedging against risks. In this light, it is desirable to use partial differential equations with relevant analytic and numerical techniques. Even if the partial differential equation method would generate stable security prices and Greeks for single asset options, however, it may result in the curse of dimensionality when pricing multi-asset derivatives. In this study, we make the best use of multi-scale nature of stochastic volatility to reduce the curse of dimensionality. Also, we present a transformation formula by which the pricing group parameters required for the multi-asset options in illiquid market can be calculated from the underlying market parameters.

2010 Mathematics Subject Classification: 91G20, 91G60
Key Words and Phrases: multi-asset, multi-scale, stochastic volatility, asymptotics, dimension reduction, illiquid market

⋅ 28th-A-09:50 − 10:10 Classification of eye lens type using machine learning method and neural net (Jongeun Kim, Hi Jun Choe, Gahyung Jo, Young Kee Park)

김종은*((연세대)), 최희준((연세대)), 조가형((연세대)), 박영기((YK안과의원))
Jongeun Kim*, Yonsei University, Hi Jun Choe, Yonsei University, Gahyung Jo, Yonsei University, Park Young Kee, YK Eye Clinic

In eye clinic, doctor prescribe a eye lens for people with keratoconus. Using the cornea map data, doctor can know the state of a patient and decide the proper eye lens type. we applied some machine learning method and neural net method to decide the eye lens type. In this process, we need many data samples and correct supervised diagnosis.

2010 Mathematics Subject Classification: 68T10
Key Words and Phrases: pattern recognition, decision tree, support vector machine, neural net, convolution neural network

⋅ 28th-A-10:10 − 10:30 Log data analysis (Yong-Ki Ma)

마용기((공주대))
Yong-Ki Ma, Kongju National University

Starting out by observing realtime information analysis of log data, we can understand characteristics of systems using optimal stochastic models. By using these models, we know theoretical basis about forecast, reasoning, response, and application. In this lecture, we introduce the stochastic volatility models in order to analyze the log data.

2010 Mathematics Subject Classification: 60G15
Key Words and Phrases: log data, stochastic processes, distributions

⋅ 28th-B-10:40 − 11:00 On the non-relativistic limit of pseudo-relativistic ground states (Woocheol Choi, Younghun Hong, Jinmyoung Seok)

최우철((인천대)), 홍영훈*((연세대)), 석진명((경기대))
Woocheol Choi, Incheon National University, Younghun Hong*, Yonsei University, CMAC, Jinmyoung Seok, Kyonggi University

In this talk, we consider the non-relativistic limit of ground states to the pseudo-relativistic nonlinear Hartree and Schrödinger equations. We present a systematic approach to find the (optimal) rate of convergence using the non-degeneracy of the limit.

2010 Mathematics Subject Classification: 35J20, 35J10, 35J60
Key Words and Phrases: ground state, non-relativistic limit, pseudo-relativistic operator

⋅ 28th-B-11:00 − 11:20 Asymptotic stability of the relativistic Boltzmann equation for soft potentials without angular cut-off (Jin Woo Jang, Robert M. Strain)

장진우*((기초과학연구원 - 기하학수리물리연구단)), Robert M. Strain((University of Pennsylvania))
Jin Woo Jang*, IBS - Center for Geometry and Physics, Robert M. Strain, University of Pennsylvania

We establish here global-in-time well-posedness and stability results for solutions nearby the relativistic Maxwellian to the special relativistic Boltzmann equation without angular cutoff. We work in the case of a spatially periodic box. We assume the generic soft-potential conditions on the collision kernel in that were derived by Dudy\'nski and Ekiel-Je$\dot{\text{z}}$ewska (Commun. Math. Phys. \textbf{115} (1985), no. 4, 607--629). In this physical situation, the angular function in the collision kernel is not locally integrable, and the collision operator behaves like a non-isotropic fractional diffusion operator.

2010 Mathematics Subject Classification: 35Q20, 35R11, 76P05, 83A05, 82C40, 35B65, 26A33
Key Words and Phrases: Boltzmann equation, special relativity, non angular cut-off, soft interaction, collisional kinetic theory

⋅ 28th-B-11:30 − 11:50 Uniform estimates with data from generalized Lebesgue spaces in periodic structures (Yunsoo Jang)

장윤수((연세대, 응용해석 및 계산센터((CMAC))))
Yunsoo Jang, Yonsei Univ., Center for Mathematical Analysis and Computation(CMAC)

We study various types of uniform Calder\'{o}n-Zygmund estimates for weak solutions in periodic homogenization. A global regularity is obtained with respect to the nonhomogeneous term form generalized Lebesgue spaces, weighted Lebesgue spaces, Orlicz spaces, and weighted Orlicz spaces, provided that the coefficients have a small BMO seminorm and the domain is a $\delta$ Reifenberg domain.

2010 Mathematics Subject Classification: 46E30, 35B27
Key Words and Phrases: homogenization, uniform estimate, weighted Lebesgue space, Orlicz space, Reifenberg domain, BMO coefficient

⋅ 28th-B-11:50 − 12:10 On maximum modulus estimates of the Navier-Stokes equations with non-zero boundary data (TongKeun Chang, Hi Jun Choe, Kyungkeun Kang)

장통근*((연세대)), 최희준((연세대)), 강경근((연세대))
TongKeun Chang*, Yonsei University, Hi Jun Choe, Yonsei University, Kyungkeun Kang, Yonsei University

We consider discontinuous influx for the Navier-Stokes flow and construct an unbounded solution near discontinuous point for any dimension bigger or equal to two. This is an extension of the result in Chang and Choe(J. Math. Fluid. Mech. {\bf 19} (2017), no. 1, 134--149) [MR3607450] that a blow-up solution exists with a bounded and discontinuous boundary data for the Stokes flow. It turns out that Dini continuity in space or log-Dini continuity in time of the normal component of boundary data is crucial for maximum modulus estimates.

2010 Mathematics Subject Classification: 35D30
Key Words and Phrases: Navier-Stokes equations, boundary value problem, maximum principle
q-Combinatorics : Enumeration and Arithmetic

⋅ 28th-B-10:40 − 11:00 Basic hypergeometric summations from rook theory (Meesue Yoo, Michael Schlosser)

유미수*((성균관대)), Michael Schlosser((University of Vienna))
Meesue Yoo*, Sungkyunkwan University, Michael Schlosser, University of Vienna

We employ a one-variable extension of $q$-rook theory to give combinatorial proofs of some basic hypergeometric summations, including the $q$-Pfaff-Saalschutz summation. This is a joint work with Michael Schlosser.

2010 Mathematics Subject Classification: 05A19, 05A15
Key Words and Phrases: basic hypergeometric series, $q$-Pfaff-Saalschutz summation, Jain summation, rook numbers

⋅ 28th-B-11:00 − 11:20 Generalization of Catalan numbers in the representation theory (Se Jin Oh, Travis Scrimshaw)

오세진*((이화여대)), Travis Scrimshaw((University of Queensland))
Se Jin Oh*, Ewha Womans University, Travis Scrimshaw, University of Queensland

In this talk, we present various generalization of Catalan numbers in aspect of representation theory. As application, we can prove the suggested problem of Katz in 2016 on composition multiplicities. This is joint work with Travis Scrimshaw in University of Queensland.

2010 Mathematics Subject Classification: 05E10, 17B37
Key Words and Phrases: Catalan number, Henkel matrix

⋅ 28th-B-11:30 − 11:50 Convolution sums of divisor functions (Daeyeoul Kim, Yoon Kyung Park)

김대열((전북대)), 박윤경*((이화여대))
Daeyeoul Kim, Chonbuk National University, Yoon Kyung Park*, Ewha Womans University

The convolution sums of divisor functions have been studied by many people and written as linear sums of divisor functions. Although these may need suitable coefficients of cusp forms - modular forms vanish at all cusps - combinatorial convolution sums are written as linear sums of divisor functions. In this talk, we study the combinatorial convolution sums involving several divisor functions and observe the result in connection with modular forms.

2010 Mathematics Subject Classification: 11A05, 11A25, 11F11
Key Words and Phrases: convolution sums, divisor functions, modular forms

⋅ 28th-B-11:50 − 12:10 Lattice paths and restricted integer partitions (Byungchan Kim)

김병찬((서울과학기술대))
Byungchan Kim, Seoul National University of Science and Technology

We introduce a relation between lattice paths and restricted partitions. After introducing a $(q,t)$-version of Delannoy paths and related open questions, a problem to find a proper Catalan analogue will be suggested.

2010 Mathematics Subject Classification: 11P81, 05A17
Key Words and Phrases: restricted partitions, lattice paths, Delannoy numbers, Catalan numbers, q-series
Kinetic Theory and Fluid Dynamics

⋅ 28th-A-09:00 − 09:20 A particle model for the herding phenomena induced by dynamic market signals (Hyeong-Ohk Bae, Seung-Yeon Cho, Sang-Hyeok Lee, Seok-Bae Yun)

배형옥((아주대)), 조승연*((성균관대)), 이상혁((아주대)), 윤석배((성균관대))
Hyeong-Ohk Bae, Ajou University, Seung-Yeon Cho*, Sungkyunkwan University, Sang-Hyeok Lee, Ajou University, Seok-Bae Yun, Sungkyunkwan University

In this paper, we study the herding phenomena arising from the combined effect of (1) non-coordinated collective interaction between the market players and (2) concurrent reactions of market players to dynamic market signals. By interpreting the expected rate of return of an asset and the favorability on that asset as position and velocity in phase space, we construct an agent based particle model for herding behavior in finance. We then define two types of herding functional using this model, and show that they satisfy Gronwall type estimates and La Salle type invariance property respectively, leading to the herding behavior of the market players.

2010 Mathematics Subject Classification: 34D05
Key Words and Phrases: herding behavior, expected rate of return, favorability, interaction, dynamic market signal

⋅ 28th-A-09:20 − 09:40 Emergent behaviors of the Schrodinger-Lohe model on cooperative-competitive network (Dohyun Kim, Hyungjin Huh, Seung-Yeal Ha)

김도현*((서울대)), 허형진((중앙대)), 하승열((서울대))
Dohyun Kim*, Seoul National University, Hyungjin Huh, Chung-Ang University, Seung-Yeal Ha, Seoul National University

The Schrodinger-Lohe (S-L) model describes the dynamics of quantum oscillators on the nodes of a quantum network which can exhibit quantum synchronization. We present several sufficient conditions which lead to the quantum synchronization under various network types. Most of the studies mainly focus on the all-to-all network, whereas we employ the cooperative-competitive network whose effect enriches the emergent behaviors, for instance, existence of closed orbit or bi-flocking-type phenomenon.

2010 Mathematics Subject Classification: 82C10, 82C22, 35B37
Key Words and Phrases: correlation function, emergence, Schrodinger-Lohe mdoel, quantum synchronization

⋅ 28th-A-09:50 − 10:10 PDEs in climate sciences (Hantaek Bae)

배한택((울산과학기술원))
Hantaek Bae, Ulsan National Institute of Science and Technology (UNIST)

In this talk, we briefly introduce some PDEs in climate sciences. These PDEs are derived from the primitive equations. More precisely, we generate the first barotropic-baroclinic equations which are the first and second modes in the Fourier series representation of the primitive equations. Under some suitable simplifications, we formulate the first barotropic-baroclinic equations in the free boundary problem setting.

2010 Mathematics Subject Classification: 76U05, 35Q35
Key Words and Phrases: primitive equations, Barotropic-baroclinic equations, free boundary problem

⋅ 28th-A-10:10 − 10:30 On contraction of Navier-Stokes shocks and uniqueness of Euler shocks (Moon-Jin Kang, Alexis Vasseur)

강문진*((숙명여대)), Alexis Vasseur((The University of Texas at Austin))
Moon-Jin Kang*, Sookmyung Women's University, Alexis Vasseur, The University of Texas at Austin

For the compressible Euler equations, it turns out that entropy weak solutions (even for a single shock) are not unique in a class of non-BV entropy weak solutions. A long standing conjecture on uniqueness of entropy weak solutions is as follows: The compressible Euler equations admit a unique entropy weak solution in a class of vanishing viscosity solutions as inviscid limits of solutions to the associated viscous system that is compressible Navier-Stokes system. In this talk, I present a contraction property (in some sense) of any weak perturbations of viscous shocks for the isentropic Navier-Stokes system. The contraction of the viscous shocks does not depend on the viscosity coefficient. Therefore this provides a weak compactness for the inviscid limit problem, that is, entropic discontinuous shocks for the isentropic Euler system are stable and unique in the class of weak inviscid limits of solutions to the Navier-Stokes system.

2010 Mathematics Subject Classification: 35L65, 35L67
Key Words and Phrases: Isentropic Euler equations, shock wave, uniqueness, inviscid limit

⋅ 28th-B-10:40 − 11:00 Existence of regular solutions for a certain type of non-Newtonian Navier-Stokes equations (Kyungkeun Kang, Hwa Kil Kim, Jae Myoung Kim)

강경근((연세대)), 김화길((고등과학원)), 김재명*((서울대))
Kyungkeun Kang, Yonsei University, Hwa Kil Kim, Korea Institute for Advanced Study, Jae Myoung Kim*, Seoul National University

We are concerned with existence of regular solutions for non-Newtonian fluids in dimension three. For a certain type of non-Newtonian fluids we prove local existence of unique regular solutions, provided that the initial data are sufficiently smooth. Moreover, if the $H^3$-norm of initial data is sufficiently small, then the regular solution exists globally in time.

2010 Mathematics Subject Classification: 76A05, 76D05, 49N60
Key Words and Phrases: non-Newtonian fluid, Navier-Stokes equations, regular solution

⋅ 28th-B-11:00 − 11:20 On a positive decomposition of entropy production functional for the polyatomic BGK model (Sa Jun Park, Seok-Bae Yun)

박사준((성균관대)), 윤석배*((성균관대))
Sa Jun Park, Sungkyunkwan University, Seok-Bae Yun*, Sungkyunkwan University

In this talk, we show that the entropy production functional for the polyatomic ellipsoidal BGK model can be decomposed into two non-negative parts. Two applications of this property: the H-theorem for the polyatomic BGK model and the weak compactness of the polyatomic ellipsoidal relaxation operator, are discussed.

2010 Mathematics Subject Classification: 35Q20
Key Words and Phrases: BGK model, Boltzmann equation, polyatomic gases, kinetic theory of gases, entropy production functional, H-theorem

⋅ 28th-B-11:30 − 11:50 Synchronization of Kuramoto oscillators with adaptive couplings (Se Eun Noh)

노세은((명지대))
Se Eun Noh, Myongji University

We study the synchronization of Kuramoto oscillators with adaptive coupling in interacting networks. Network dynamics preserves the sum of all incoming pairwise coupling strengths and is designed to adaptively interact with system dynamics. For adaptive couplings, we use two adaptive coupling laws for the pairwise coupling strength. Kuramoto oscillators are assumed to be on the nodes of the networks. We present frameworks that guarantee the emergence of synchronization for various coupling feedback laws. Our results generalize earlier work on the synchronization of Kuramoto oscillators in fixed and symmetric networks.

2010 Mathematics Subject Classification: 70F99, 92B25
Key Words and Phrases: Kuramoto oscillators, adaptive couplings

⋅ 28th-B-11:50 − 12:10 Quasi-neutral limit for the Euler-Poisson system (Bongsuk Kwon, Chang-Yeol Jung, Masahiro Suzuki)

권봉석*((울산과학기술원)), 정창열((울산과학기술원)), Masahiro Suzuki((Nagoya Institute of Technology))
Bongsuk Kwon*, UNIST, Chang-Yeol Jung, UNIST, Masahiro Suzuki, Nagoya Institute of Technology

We investigate the existence, time-asymptotic behavior, and quasi-neutral limit of the boundary layer solutions for the Euler-Poisson equations in the three dimensional annular domain. If time permits, some key features of the proof and related problems will be discussed. This is a joint work with C.-Y. Jung (UNIST) and M. Suzuki (Nagoya Inst. Tech.).

2010 Mathematics Subject Classification: 35
Key Words and Phrases: Euler-Poisson equations
Quantum Information, Computation and Cryptography

⋅ 28th-A-09:00 − 09:20 Separability of multi-qubit X-states (Seung-Hyeok Kye)

계승혁((서울대))
Seung-Hyeok Kye, Seoul National University

We characterize separability of multi-qubit X-shaped states. This class includes many important states like Greenberger-Horne-Zeilinger diagonal states. Our characterization also gives rise to a necessary criterion for general multi-qubit states which is strong enough to detect PPT entanglement of nonzero volume. This is based on several coworks with Lin Chen, Kil-Chan Ha and Kyung Hoon Han.

2010 Mathematics Subject Classification: 81P15
Key Words and Phrases: separable, entangled, multi-qubit, X-states

⋅ 28th-A-09:20 − 09:40 State transfer with quantum side information (Yonghae Lee, Soojoon Lee)

이용해*((경희대)), 이수준((경희대))
Yonghae Lee*, Kyung Hee University, Soojoon Lee, Kyung Hee University

We first consider quantum communication protocols between a sender Alice and a receiver Bob, which transfer Alice's quantum information to Bob by means of non-local resources, such as classical communication, quantum communication, and entanglement. In these protocols, we assume that Alice and Bob may have quantum side information, not transferred. In this work, these protocols are called the state transfer with quantum side information. We determine the optimal costs for non-local resources in the protocols, and show that if Alice or Bob exploits more quantum side information in the protocols, then they can perfectly perform the protocols with lower resource costs. Furthermore, our results can give new operational meanings to the quantum mutual information and the quantum conditional mutual information, which directly provide us with an operational interpretation of the chain rule for the quantum mutual information.

2010 Mathematics Subject Classification: 81P45
Key Words and Phrases: quantum information, quantum side information, quantum communication

⋅ 28th-A-09:50 − 10:10 Quantum secret sharing and mermin operator (Minjin Choi, Yonghae Lee, Soojoon Lee)

최민진*((경희대)), 이용해((경희대)), 이수준((경희대))
Minjin Choi*, Kyung Hee University, Yonghae Lee, Kyung Hee University, Soojoon Lee, Kyung Hee University

We present a quantum secret sharing protocol on a given state close to the Greenberger-Horne-Zeilinger state, and use an inequality derived from the Mermin inequality to determine whether players in our protocol securely achieve perfectly correlated classical bits. In this work, we show that if our inequality holds then every legitimate player can have key bits with positive key rate. Therefore, for sufficiently many copies of the state, the players can securely share a classical secret with high probability by our protocol.

2010 Mathematics Subject Classification: 81P45, 81P94
Key Words and Phrases: quantum cryptography, secret sharing, Mermin operator

⋅ 28th-A-10:10 − 10:30 A quantum cellular automaton for quantum electrodynamics (Cedric Beny, Pablo Arrighi, Terry Farrelly)

Cedric Beny*((한양대)), Pablo Arrighi((Aix-Marseille University)), Terry Farrelly((Leibniz University, Hannover))
Cedric Beny*, Hanyang University ERICA, Pablo Arrighi, Aix-Marseille University, Terry Farrelly, Leibniz University, Hannover

A QCA is a model of unitary dynamics in discrete space and time. Since this is just a local quantum circuit, it can be naturally implemented on a quantum computer, or potentially on a quantum simulator. We built a QCA which simulates quantum electrodynamics in one dimension of space (Schwinger model). The QCA is built from first principles, and is itself intelligible without reference to the quantum field theory. It also has the potential to generalize to higher dimensions and other gauge groups.

2010 Mathematics Subject Classification: 81P68, 68Q80, 81V10, 81T80
Key Words and Phrases: quantum cellular automaton, quantum electrodynamics, quantum simulations, lattice gauge theory

⋅ 28th-B-10:40 − 11:00 Distinguishability, ensemble steering, and the no-signaling principle (Joonwoo Bae)

배준우 ((한양대))
Joonwoo Bae, Hanyang University

We consider a fundamental operational task, distinguishing systems in different states, in the framework of generalized probabilistic theories and provide a general formalism of minimum-error discrimination of states in convex optimization. With the formalism established, we show that the distinguishability is generally a global property assigned to the ensemble of given states rather than other details of a given state space or pairwise relations of given states. Then, we consider bipartite systems where ensemble steering is possible, and show that show that with two operational tasks, ensemble steering and the no-signaling condition, the distinguishability is tightly determined. The result is independent to the structure of the state space. This concludes that the distinguishability is generally determined by the compatibility between two tasks, ensemble steering on states and the non-signaling principle on probability distributions of outcomes.

2010 Mathematics Subject Classification: 81P94, 81P45, 81P16
Key Words and Phrases: quantum cryptography, quantum information theory, quantum correlations