엄상일   Sang-il Oum 
    

• 기초과학연구원 이산수학그룹 CI
   CI, Discrete Mathematics Group (DIMAG), Institute for Basic Science (IBS)  

• 한국과학기술원 수리과학과 교수
   Professor, Department of Mathematical Sciences, KAIST

Title: How to decompose a graph into a tree-like structure

Many NP-hard problems on graphs are known to be tractable if we restrict the input to have a certain decomposition into a tree-like structure.
Width parameters of graphs are measures on how easy it is to decompose the input graph into a tree-like structure.
The tree-width is one of the most well-studied width parameters of graphs and the rank-width, proposed by the speaker and Seymour about 15 years ago, is a generalization of tree-width into dense graphs.
This talk will present a survey on width parameters of graphs such as tree-width and rank-width and discuss how we can find a decomposition of an input graph
into a tree-like structure efficiently.

채수찬   Suchan Chae
         

• 한국과학기술원 기술경영학부 교수
   Professor, Department of Business and Technology Management, KAIST

• 한국과학기술원 대외부총장
   Vice President for Planning and Budget, KAIST

Title: 사회과학의 수학적 접근 – 경제학과 수학 –

사회과학의 수학적 접근은 합리적인 인간행위라는 공리로부터 출발한다. 주어진 환경하에서 한 개인이나 기업이 목표치를 최대화하는 행위는 다양한 수학적 프로그래밍으로 접근한다. 복수의 개인이나 기업이 협력과 경쟁이 공존하는 환경하에서는 상호의존적 행위는 게임이론의 다양한 해개념으로 접근한다. 이러한 접근의 기초를 설명하고 몇 가지 모델을 사례로 이야기한다.

김명환   Myung-Hwan Kim
         
• 서울대학교 자연과학대학 수리과학부 교수
   Professor, Department of Mathematical Sciences, Seoul National University

• 한국학술단체총연합회 회장
   President, The Association of Korean Academic Societies

Title: 수학의 시대정신(?)

일각에서 혁명이라고 칭할 정도로 4차 산업은 미래 사회를 송두리째 변혁시킬 것으로 예견되고 있다. 이러한 대변혁의 시기를 맞아 우리나라 수학의 미래를 위해, 우리 수학계가 처한 위기와 기회를 파악하고, 나아갈 방향과 방책에 대한 논의를 시작해 보고자 한다.

[대수학 Algebra]  김범식   Bumsig Kim
    

• 고등과학원 수학부 교수
  Professor, School of Mathematics, Korea Institute for Advanced Study (KIAS)

Title: Hochschild Homology of GLSM

A Landau-Ginzburg model is a smooth DM stack X with a regular function w or more generally, a section w of a line bundle on X.  There is a notion of  factorizations for w which plays the role of complexes of sheaves. When the Landau-Ginzburg model is a gauged linear sigma model, we compute Hochschild homology. This is based on joint work with Ionut Ciocan-Fontanine (Univ. of Minnesota), David Favero (Univ. of Alberta), Jeremey Guere (Grenobel Alpes Univ.), Mark Shoemaker(Colorado State Univ.).

[해석학 Analysis]  옥지훈   Jihoon Ok     
   

• 경희대학교 응용수학과 교수
  Professor, Department of Applied Mathematics, Kyung Hee University

• 2018년도 대한수학회 상산젊은수학자상 수상자
  The winner of 2018 Sangsan Prize for Young Mathematicians 

Title: Maximal regularity for local minimizers of non-autonomous functionals

We establish local $C^{1,\alpha}$-regularity for some $\alpha\in(0,1)$ and $C^{\alpha}$-regularity for any $\alpha\in(0,1)$ of local minimizers of the functional
$$v\ \mapsto\ \int_\Omega \varphi(x,|Dv|)\,dx,$$where $\varphi$ satisfies a $(p,q)$-growth condition. Establishing such a regularity theory with sharp, general conditions has been an open problem since the 1980s In contrast to previous results, we formulate the continuity requirement on $\varphi$ in terms of a single condition for the map $(x,t)\mapsto \varphi(x,t)$, rather than separately in the $x$- and $t$-directions. Thus we can obtain regularity results for functionals without assuming that the gap between the upper and lower bounds is small, i.e.\ $\frac qp$ need not be close to $1$. Moreover, for $\varphi(x,t)$ with particular structure, including $p$-, Orlicz-, $p(x)$- and double phase-growth, our single condition implies known, essentially optimal, regularity conditions. Hence we handle regularity theory for the above functional in a universal way.
  
[This is joint work with Peter Hästö(University of Turku).]

[기하학 Geometry]  호팍통   Pak Tung Ho     
   

• 서강대학교 자연과학부 수학과 교수
  Professor, School of Natural Sciences, Sogang University

• 2018년도 대한수학회 봄 논문상 수상자
  The winner of 2018 Excellent Research Paper Award

Title: Prescribing curvature in the presence of symmetry

In this talk, I will talk about the flow approach of studying the prescribing curvature problem. In particular, I will explain some existence results of the prescribing curvature problem when the curvature function possesses certain symmetry. 

[위상수학 Topology]  백형렬   Hyungryul Baik
    

• 한국과학기술원 수리과학과 교수 
  Professor, Department of Mathematics, KAIST

• 2018년도 대한수학회 상산젊은수학자상 수상자
  The winner of 2018 Sangsan Prize for Young Mathematicians

   
Title: Normal generators for mapping class groups are abundant in the fibered cone
We show that for almost all primitive integral cohomology classes in the fibered cone of a closed fibered hyperbolic 3-manifold, the monodromy normally generates the mapping class group of the fiber. Key idea of the proof is to use Fried’s theory of suspension flow and dynamic blow-up of Mosher. If the time permits, we also discuss the non-existence of the analogue of Fried’s continuous extension of the normalized entropy over the fibered face in the case of asymptotic translation lengths on the curve complex.

[This is joint work with Eiko Kin(Osaka University), Hyunshik Shin(University of Georgia), Chenxi Wu(Rutgers University).]

[확률·통계학 Probability and Statistics]  정폴   Paul Jung           
       

• 한국과학기술원 수리과학과 교수 
  Professor, Department of Mathematics, KAIST 

• 2018년도 대한수학회 봄 논문상 수상자
  The winner of 2018 Excellent Research Paper Award

Title:  A Generalization of Hierarchical Exchangeability on Trees to Directed Acyclic Graphs

Motivated by problems in Bayesian nonparametrics and probabilistic programming discussed in Staton et al. (2018), we present a new kind of partial exchangeability for random arrays which we call DAG-exchangeability. In our setting, a given random array is indexed by certain subgraphs of a directed acyclic graph (DAG) of finite depth, where each nonterminal vertex has infinitely many outgoing edges. We prove a representation theorem for such arrays which generalizes the Aldous-Hoover representation theorem.
In the case that the DAGs are finite collections of certain rooted trees, our arrays are hierarchically exchangeable in the sense of Austin and Panchenko (2014), and we recover the representation theorem proved by them. Additionally, our representation is fine-grained in the sense that representations at higher levels of the hierarchy are also available. This latter feature is important in applications to probabilistic programming, thus offering an improvement over the Austin-Panchenko representation even for hierarchical exchangeability.

[응용수학 Applied Mathematics]  김혜현   Hyea Hyun Kim           
            

• 경희대학교 응용수학과 교수
  Professor, Department of Applied Mathematics, Kyung Hee University

Title: Domain decomposition preconditioners for multiscale problems

A two level overlapping Schwarz method is proposed for fast solutions of an algebraic system of an elliptic problem with multiscale coefficients. The algebraic system is obtained from finite element discretization. The condition number of the resulting algebraic system depends on the contrast in the multiscale coefficients and the mesh size in the finite element discretization.
As a fast solver, an iterative method is applied to the algebraic system combined with a domain decomposition preconditioner. For the domain decomposition preconditioner, a two level overlapping Schwarz preconditioner is proposed by utilizing constrained energy minimizing multiscale finite element functions as a coarse basis. The constrained energy minimizing multiscale finite element functions are developed in a recent work by the second author and they are shown to provide a coarse approximation that is more robust to the variations in the coefficients. In addition, the proposed functions have some nice orthogonal properties and an exponential decay  property. In our work, using such nice properties we can show that the proposed preconditioner equipped with the new coarse basis is also robust to the variations in the coefficients and to the overlapping width in the subdomain partition. 
Numerical results are included to confirm the theory and to  present the performance of the proposed method.

  
[This is joint work with Eric Chung (The Chinese University of Hong Kong), Junxian Wang (Xiangtan University).]

[수학교육 Mathematical Education]  김수환   Soohwan Kim           
            

• 청주교육대학교 수학교육과 교수
  Professor, Department of Mathematics Education, Cheongju National University of Education

Title:  What will be taught in the era of the Fourth Industrial Revolution?

In order to foster the core competencies that all learners can actively respond to in the era of the Fourth Industrial Revolution, learners should be able to lead and solve problems in all courses. In addition, there is an urgent need to improve convergent lectures that can utilize various software and smart devices. In reality, however, educational practices are emphasizing too much emphasizing the inherent characteristics of each lecture. In order to improve this, it is necessary to make and present a smart learning model by presenting and discussing the case of each lecture by the professors in charge of each lecture.
In this lecture, we will try to create a forum where participants will share their opinions, focusing on lectures by lecturers. To this end, we seek ways to share the opinions of many people using okmindmap and mentimeter.com. In addition, we have contributed greatly to the development of mathematics and mathematics education in the future by utilizing the experience of Korean mathematic educators and mathematicians who successfully hosted the 12th International Conference on Mathematics Education in 2012 and the International Mathematicians Conference in 2014. I look forward to your contribution and I urge you.

[이산수학 Discrete Mathematics]  신희성   Heesung Shin           
            

• 인하대학교 자연과학대학 수학과교수
  Professor, Department of Mathematics, Inha University

Title:  Symmetric unimodal expansions of Eulerian polynomials
In this talk, we consider several generalizations of the classical $\gamma$-positivity of Eulerian polynomials using generating functions and combinatorial theory of continued fractions. For the symmetric group, we prove an expansion formula for inversions and excedances as well as a similar expansion for derangements. We prove the $\gamma$-positivity for Eulerian polynomials for derangements of type $B$. We also gives more general expansion formulae of Eulerian polynomials for $r$-colored derangements, which answer and generalize several open problems in the literature.

[암호학 Cryptography]  김명선   Myungsun Kim   
   

• 수원대학교 ICT융합대학 정보통신학부 교수
  Professor, Department of Information Security, The University of Suwon

Title:  Recent results on verifiable computations
In this talk, I will provide a brief survey about verifiable computation. Verifiable computation (VC) has been one of main topics in theoretical computer sciences, especially in complexity theory. The main reason for such importance is the wide applicability of VC; for example cloud computing. In the literature, since after Goldwasser-Kalai-Rothblum's remarkable work to efficiently evaluating arithmetic circuits  this topic has gained lots of interests. Recently there have been known much improvements. Thus in this talk I will introduce key results and their conceptual workflow along with interesting applications.