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

Title: Topology, group action and geometry
In this talk, we will try to explain how to use group actions, geometric structures and other geometric objects to understand the topology of a manifold. Such an approach has many successful stories in Thurston's geometrization program, Gromov's simplicial volume and surface group representation theory. We will try to describe them briefly during the talk.

김종락   Kim, Jon-Lark
        
• 서강대학교 수학과 교수
   Professor, Department of Mathematics, Sogang University

   
Title: 수학적 게임에서 인공지능까지 (From mathematical games to Artificial Intelligence)

앨런 튜링, 존 폰 노이만, 클로드 섀넌의 공통점은 무엇일까? 초기 컴퓨터와 인공지능 발전에 획기적인 공헌을 한 사람들로 알려져 있다. 하지만 또 다른 공통점은 그들은 수학적 게임에 심취해 있었다는 것이다. 이번 강연에서는 많은 수학자들이 아직 접해보지 못한 다양한 수학적 게임들을 소개하고자 한다. 조합론을 이용한 세트 게임과 1258 게임, 선형대수를 활용한 라이트 아웃, 클라인 4-그룹을 이용한 페그 솔리테어, 부분순서집합을 이용한 촘프 게임과 님 게임 등을 소개하고자 한다. 또한 온라인 보드판에서 펼쳐지는 수학 개념 게임인 매트리킹을 소개한다. 끝으로 어떤 게임이 인공지능 기반 게임으로 발전할 수 있는지 논의한다.

What do Alan Turing, John von Neumann and Claude Shannon have in common? It is known that they contributed remarkably to early computer and artificial intelligence development. But another common thing is that they were attracted to mathematical games. This lecture introduces a variety of mathematical games that many mathematicians have not yet encountered. We will introduce SET game and 1258 game using combinatorics, Light Out using linear algebra, Peg Solitaire using Klein's 4-group, and Chomp game and Nim game using partially order sets. We also introduce MaTricKing, an online mathematical concept game on board. We further discuss  which games can evolve into artificial intelligence-based games.

Jann-Long Chern      
      

• Professor, Department of Mathematics, National Central University,
  Taiwan   

  
Title: On the Hardy-Sobolev type elliptic equations with multiple boundary  singularities and Caffarelli-Kohn-Nirenberg inequality

In this talk we are interested in how the geometry of boundary singularities can affect the existence of positive solutions of elliptic equations.  In particular, we study the Dirichlet problem for an elliptic equation with multiple singularities on the boundary of a domain. In many nice results,  the conditions on curvature approach have been  extensively explored in several different cases to study the existence of positive solutions of such kind problems. In this talk we propose a  more general criterion to study the existence result by  the concept of contact order. This new contact order approach provides a refined way to analyze boundary singularities, and includes the curvature approach  as a special case. A novel feature here is that we are able to obtain positive results for convex domains such as a ball, a half sphere or a rectangular box which are unreachable by the standard curvature method.   Our second theorem  is a non-existence result which suggests that our previous existence result is optimal for certain convex domains. This type of optimality  is  rarely addressed in literature. In the third part of this talk, we generalize the above theorems to $N=3$ and show the existence of minimizers for the  Caffarelli-Kohn-Nirenberg inequalities when $N=3$--this solves the problem left open in [Chern and Lin, 2010 ARMA], hence completing a long line of research.
 
This talk are based on the joint works with X. Fang and C. Hsia, and C.-S. Lin respectively.

[대수학 Algebra]  박지훈   Park, Jihun
   

• 포항공과대학교 수학과 교수
  Professor, Department of Mathematics, Pohang University of Science and
  Technology (POSTECH)
• 2017년도 대한수학회상 봄 논문상 수상자 
  The winner of 2017 Excellent Research Paper Award
    

Title: Asymptotic invariants of Fano varieties
The plurianticanonical linear systems of a given Fano variety carry abundant information on geometry of the Fano variety. In particular, the singularities of the linear system reflect many essential features of the Fano variety. These singularities can be measured by log canonical thresholds. Using log canonical thresholds we can define useful invariants that indicate several important properties of Fano varieties. In this talk
I review such  invariants  defined in asymptotic ways.  Also their applications will be introduced. 

[해석학 Analysis]  오성진   Oh, Sung-Jin     
   

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

Title: The threshold theorem for the hyperbolic Yang-Mills equation

In this talk, I will present the recent proof of the Threshold Theorem for the energy critical hyperbolic Yang-Mills equation in (4+1) dimensions. In particular, we give sharp criteria for global existence and scattering in terms of the energy of the initial data, as well as in terms of bubbling-off a harmonic Yang-Mills connection.

Our proof lies at the intersection of many recent developments, including null form estimates and function spaces; parametrix construction via gauge renormalization; induction on energy; monotonicity formulae arising from the normalized scaling vector field etc. Also of note is the use of the associated parabolic flow, namely the Yang-Mills heat flow, to construct a high quality global gauge (called the caloric gauge), extending the idea of Tao for the harmonic map heat flow.
  
[This is a joint work with D. Tataru (UC Berkeley)]

[기하학 Geometry]  강현석   Kang, Hyunsuk

• 광주과학기술원 기초교육학부 교수
   Professor, Division of Liberal Arts and Sciences, Gwangju institute of
   Science and Technology (GIST)

Title: Differential Harnack inequality for curvature flows
Based on the inspiring works of Li and Yau on parabolic kernel on Riemannian manifolds and of Hamilton using the maximum principle, differential Harnack inequality has been crucial in understanding the geometry and analysis of curvature flows such as mean curvature flow and Ricci flow.  For example, this leads to compare the solution of a curvature flow at different points and time, which can be also achieved by space-time constructions.  By considering more general curvature flows with the speed determined by curvature function of homogeneous degree one, similar inequalities can be obtained and we will review the development of this topic.

[위상수학 Topology]  김세구   Kim, Se-Goo
   

• 경희대학교 수학과 교수
   Professor, Department of Mathematics, Kyung Hee University

   
Title: Concordance invariants from knot Floer homology
Since the birth of knot Floer homology defined by Ozsváth-Szabó and Rasmussen, several concordance invariants have been defined and studied from this theory. Examples are the $\tau$ invariant of Ozsváth-Szabó, the $\delta$ invariant of Manolescu-Owens, the $d$ obstruction of Grigsby-Ruberman-Strle, the $\epsilon$ invariant of Hom, the $\nu^+$ invariant of Hom-Wu, the $\Upsilon$ invariant of Ozsváth-Szabó and the $\Upsilon^2$ invariant of Kim-Livingston. We briefly introduce some of these invariants and present their properties.

[확률 및 통계학 Probability and Statistics]  이지운   Lee, Ji Oon           
       

• 카이스트 수리과학과 교수     
   Professor, Department of Mathematical Sciences, Korea Advanced Institute
   of Science and Technology Constitution (KAIST)
• 2017년도 대한수학회상 봄 논문상 수상자
   The winner of 2017 Excellent Research Paper Award

Title: Spherical Spin Glass with Ferromagnetic Interaction
We consider the spherical Sherrington-Kirkpastrick model with ferromagnetic Curie-Weiss interaction. Using recent results of random matrix theory, we prove the limiting distributions of the free energy for all parameters. As an intermediate step, we also establish a central limit theorem for the linear statistics of rank 1 spiked symmetric random matrices. This is a joint work with Jinho Baik.

[응용수학 Applied Mathematics]  신동욱   Shin, Dong-wook     
   

• 연세대학교 응용해석 및 계산센터 연구원
   Postdoctoral researcher, Center for Mathematical Analysis and
   Computation, Yonsei University
    

Title: High-order methods and adaptive algorithms
In this talk, we consider the high-order methods such as finite element method (FEM), mixed FEM, discontinuous Galerkin (DG) method, and hybrid DG method. Typically, high-order methods allow to achieve high-order accuracy with high-order approximations. However, the order of accuracy depends on the regularity of the exact solution. Thus, high-order accuracy is not accomplished if the exact solution has low regularity. Adaptive algorithms are efficient to compute numerical solutions for non-smooth solutions or in the presence of boundary or internal layers. A key ingredient of adaptive algorithms is the error estimator obtained from a posteriori error estimates. An adaptive algorithm consists of successive loops of the form, SOLVE $\rightarrow$ ESIMATE $\rightarrow$ MARK $\rightarrow$ REFINE. In this procedure, high-order accuracy is achieved in terms of degrees of freedom.

[수학교육 Mathematical Education]  김용운   Kim, Yong Woon

• 수학문화연구소 연구소장
• 한양대학교 수학과 명예교수
  Emeritus Professor, Department of Mathematics, Hanyang University

Title: 수학사학의 의미
수학체계는 그 내부의 논리에 의해서만 발달하므로 외부체계는 일절 개입할 수 없다. 그러나 대부분 수학의 가설과 모델은 외부의 경제, 정치, 사회 문제와 관련되어 있다. 가령 D. Hilbert의 「수학기초론」은 동시대의 Saussure의 「언어구조론」, N. Chomsky의 「생성문법론」, Levi-Straus의 「친족구조론」 등과 같이 시대적 구조주의 철학과 맥을 같이 한다. 마르크스주의자는 수학을 ‘사회경제적 기초’ 위에 있는 상부구조의 하나로 간주한다. 그러나 수학은 단순한 경제의 상부구조이거나 독립변수가 아니며 개방계로서 밀접한 ‘되먹임 관계(feed back loop)’로 ‘원형=집단무의식’과 이어져 있으며, 또한 이들 관계는 수학사학의 중요과제다. 본 연구자는 이상의 수학과 문화의 관계를 관찰하는 ‘원형(原型)사관’을 제안하고, 수학사의 범위와 내적 수학사와 외적 수학사의 차이를 설명하여 수학사학의 체계화 가능성을 제시하고 끝으로 S. P. Snow가 제기한 두 개의 문명, 자연과학과 사회인문학에 관한 관계에 대한 접근을 시도한다.

[이산수학 Discrete Mathematics]  이상준   Lee, Sang June       

• 덕성여자대학교 수학과 교수
   Professor, Department of Mathematics, Duksung Women's University

Title: Infinite Sidon sets contained in sparse random sets of integers

A set $S$ of natural numbers is a \emph{Sidon} set if all the sums $s_1+s_2$ with $s_1$, $s_2\in S$ and $s_1\leq s_2$ are distinct. Let constants $\alpha>0$ and $0<\delta<1$ be fixed, and let $p_m=\min\{1,\alpha m^{-1+\delta}\}$ for all positive integers $m$. Generate a random set $R\subset\mathbb N$ by adding $m$ to $R$ with probability $p_m$, independently for each $m$.  We investigate how dense a Sidon set $S$ contained in $R$ can be.  Our results show that the answer is qualitatively very different in at least three ranges of $\delta$.  We prove quite accurate results for the range $0<\delta\leq2/3$, but only obtain partial results for the range $2/3<\delta\leq1$. 

[암호학 Cryptography]  이형태   Lee, Hyung Tae  
   

• 전북대학교 컴퓨터공학부 교수
  Professor, Division of Computer Science and Engineering, Chonbuk 
  National University

Title: Private Compound Wildcard Queries using Fully Homomorphic Encryption

In this talk, we will look into a private database query (PDQ) protocol that supports compound wildcard queries on encrypted databases using fully homomorphic encryption. To this end, we will first develop an algorithm for testing whether an encrypted string contains an encrypted pattern without revealing any information of the pattern, taking auxiliary encryptions as additional input. On top of this, we then propose a PDQ protocol for compound queries using wiildcard search conditions. Finally, we give proof-of-concept implementation results of the proposed PDQ protocol.
 
(This is joint work with Myungsun Kim, San Ling, Benjamin Hong Meng Tan, and Huaxiong Wang.)