2015. 4. 24(금) ~ 26(일), 부산대학교
◎ Plenary Lecture (4.25(토))
변재형 Byeon, Jaeyoung |
◎ Public Lecture (4.24(금))
김영욱 Kim, Young Wook |
◎ Invited Lectures (4.25(토))
[Algebra] 현동훈 Hyeon, David Donghoon • 서울대학교 자연과학대학 수리과학부 교수 Professor, Department of Mathematical Sciences, Seoul National University • 2014년도 대한수학회상 봄 논문상 수상자 The winner of 2014 Excellent Research Paper Award Title: Generic semistability for actions of reductive groups Given an algebraic group $G$ and a rational representation $\rho: G \to GL(V)$, a point $v \in V$ is said to be semistable if the closure of the $G$-orbit of $v$ does not contain the origin. For reductive groups, the Hilbert-Mumford theorem states that $v$ is unstable if and only if there is a co-character $\lambda$ of $G$ such that $\lim_{t\to 0} \lambda(t).v = 0$. It has long been observed by the researchers that, to find a destabilizing co-character, one has to choose a maximal torus carefully. In this talk, we shall present a framework in which this observation can be made precise in the semisimple case, and how it can be generalized for the reductive groups. This is joint work with J. Park and D. Ph. Bac. |
[Analysis I] 고응일 Ko, Eungil • 이화여자대학교 자연과학대학 수리물리과학부 수학전공 교수 Professor, Department of Mathematics, Ewha Womans University • 2014년도 대한수학회상 학술상 수상자 The winner of 2014 KMS Academic Achievement Award Title: Invariant subspace problem and weighted composition operators Let $\cal{H}$ be a separable, infinite dimensional, complex Hilbert space and let $\cal{L}(\cal{H})$ be the algebra of all bounded linear operators on $\cal{H}$. We give some theorems about the invariant subspace problem by using the Aluthge transforms. By studying some weighted composition operators, we discuss that the resulting ideas can be used to find the Aluthge transforms in Hardy spaces. |
[Analysis II] 김성연 Kim, Sung Yeon • 강원대학교 사범대학 수학교육과 교수 Professor, Department of Mathematics Education, Kangwon National University • 2014년도 대한수학회상 봄 논문상 수상자 The winner of 2014 Excellent Research Paper Award Title: Rigidity of CR maps between bounded symmetric domains The goal of this talk is to study the CR structure on the boundary components of bounded symmetric domain of type I and investigate the rigidity phenomenon for {\em locally defined CR embeddings} between boundaries of type I bounded symmetric domains of higher rank. In this talk, we follow the Cartan's moving frame method. When boundary components are other than Shilov boundary component, which are Levi-degenerate, our analysis is based on their $2$-nondegeneracy combining Levi form with higher order tensors. After showing the rigidity phenomenon of CR maps, we study rigidity phenomenon for proper holomorphic maps between bounded symmetric domains of type I. |
[Geometry] 김종수 Kim, Jongsu • 서강대학교 이과대학 수학과 교수 Professor, Department of Mathematics, Sogang University Title: Deformation of Riemannian metrics which decreases the scalar curvatures In this talk, some deformations of Riemannian metrics which decrease the scalar curvatures will be discussed. After explaining previous works including Lohkamp's results, I discuss first on the scalar curvatures of almost Kaehler metrics and contact metrics. Then I will talk on the existence of a smooth family of Riemannian metrics which strictly decrease the scalar curvatures in a ball but remain unchanged away from the ball. |
[Topology] 조상범 Cho, Sangbum • 한양대학교 사범대학 수학교육과 교수 Professor, Department of Mathematics Education, Hanyang University Title: The Goeritz groups of 3-manifolds Given a genus-g Heegaard splitting of a 3-manifold, the genus-g Goeritz group is the group of isotopy classes of orientation preserving homeomorphisms of the manifold preserving the splitting. It is natural to study the structures of Goeritz groups, and so finding their generating sets or presentations has been an interesting problem. But the generating sets or the presentations of those groups have been obtained only for few manifolds with their splittings of small genus. In this talk, we look over a brief history of this problem and introduce its recent progress together with some applications. |
[Probability and Statistics] 이지운 Lee, Ji Oon • 카이스트 자연과학대학 수리과학과 교수 Professor, Department of Mathematical Sciences, KAIST(Korea Advanced Institute of Science and Technology) • 2014년도 대한수학회 상산 젊은수학자상 수상자 The winner of 2014 Sangsan Prize for young Mathematicians Title: Tracy-Widom Distribution for Sample Covariance Matrices Consider a sample covariance matrix of the form $XX^*$. The sample $X$ is an $M \times N$ real random matrix whose columns are independent multivariate Gaussian vectors with covariance $\Sigma$. We show that the fluctuation of the largest rescaled eigenvalue is given by Tracy-Widom distribution for a large class of general $\Sigma$. Basic concepts and tools to analyze the eigenvalue distribution of random matrices will also be introduced. |
[Applied Mathematics] 최형인 Choi, Hyeong In |
[Mathematical Education] 노선숙 Noh, Sunsook • 이화여자대학교 사범대학 수학교육과 교수 Professor, Department of Mathematics Education, Ewha Womans University Title: A sense of purpose and responsibility for mathematics educators Everyone agrees and history has shown that mathematics is critical to the advancement of society. Quality mathematics education is essential in determining success for individuals, groups, countries and society. Therefore, the role and responsibility of mathematics educators cannot be underestimated and it can easily be described as being greater than the sum of its parts. Today, the intense debates about what and how to teach mathematics can make the educators lose sight of why we teach. In this talk, a reflection of why we teach will be discussed with the goal of establishing a renewed sense of purpose and responsibility for everyone involved in mathematics teaching at all levels of education. |
[Mathematics for Information Sciences] 박보람 Park, Boram • 아주대학교 자연과학대학 자연과학부 수학전공 교수 Professor, Department of Mathematics, Ajou University • 2014년도 대한수학회 상산 젊은수학자상 수상자 The winner of 2014 Sangsan Prize for young Mathematicians Title: On List Square Coloring Conjecture A graph $G$ is called {\em chromatic-choosable} if $\chi_l (G) = \chi(G)$. It is an interesting problem to find graphs that are chromatic-choosable. There are several famous conjectures that some classes of graphs are chromatic-choosable including the List Coloring Conjecture, which states that any line graph is chromatic-choosable. The square $G^2$ of a graph $G$ is the graph defined on $V(G)$ such that two vertices $u$ and $v$ are adjacent in $G^2$ if the distance between $u$ and $v$ in $G$ is at most 2. Let $\chi(H)$ and $\chi_l(H)$ be the chromatic number and the list chromatic number of $H$, respectively. In 2001, Kostochka and Woodall conjectured that for any graph $G$, $\chi_l(G^2)=\chi(G^2)$, which is called List Square Coloring Conjecture. The List Square Coloring Conjecture has attracted a lot of attention and been cited in many papers related with coloring problems so far, and it has been widely accepted to be true. The List Square Coloring Conjecture has been proved for several small classes of graphs. In this talk, we give counterexamples to the List Square Coloring Conjecture and then explain recent works related to it. |
[Cryptography] 이향숙 Lee, Hyang-Sook • 이화여자대학교 자연과학대학 수리물리과학부 수학전공 교수 Professor, Department of Mathematics, Ewha Womans University Title: Efficient Pairings and Pairing Friendly Curves in Cryptography Pairings on elliptic curves have been playing an important role in cryptography for long time. In this talk, we review the works regarding the efficient pairing computations and several methods for constructing the families of pairing-friendly elliptic curves. It has been also known that Type 3 pairings are overall the most efficient choice for cryptographic applications, with Type 1 pairings (symmetric pairings) comparable in some circumstances. Recent progress in the development of index calculus algorithms, and in particular of function field sieve algorithms, for computing discrete logarithms in finite fields put Type 1 pairings into less favorable position. We introduce the issues related to converting protocols based on Type 1 and 2 pairings into those Type 3 pairings counterparts. |