2011 대한수학회 정기총회 및 가을 연구발표회

<Plenary Lecture> David Burns   Professor, Department of Mathematics, King's College London (UK)   Number Theory   [Homepage] [Plenary Lecture]  16:30~17:20, October 21(Fri), 2011   Title : On main conjectures of geometric Iwasawa theory and related conjectures   We discuss the natural main conjecture of non-commutative Iwasawa theory for flat, smooth sheaves on schemes that are separated and of finite type over a finite field. We also discuss the key ideas that lay behind the recent proof of this conjecture and a range of interesting, and more explicit, consequences that this result has.       <Special Lecture> 민동필 Dongpil Min   전 기초기술연구회 이사장  Former Chairman of Korea Research Council of Fundamental Science & Technology (KRCF)   [KRCF Homepage] [Special Lecture]  15:30~16:20, October 21(Fri), 2011 Title : 국제과학비즈니스벨트와 기초과학연구원 (Basic Science Institute and ISBB) 국제과학비즈니스벨트에 들어 갈 기초과학연구원이 추구하는 핵심이 수월성이며, 따라서 좋은 과학자를 유치해서 그 창의력을 발휘할 수 있게 환경을 만들어 주는 것이다. 이를 위해 기초과학연구원은 세계의 연구자들과 젊은 과학자들에게 가고 싶고, 가담하고 싶고, 방문하고 싶은 곳이 되어야 한다. 이 국제과학비즈니스벨트 프로젝트의 취지와 그 중에 핵심이 되고 있는 기초과학연구원에 대한 기본 골격을 소개한다. 그리고 이 연구원이 담고 있는 우리의 꿈과 현실 사이의 거리를 좁혀야 하는 우리 과학계의 노력과 그 방향을 살펴본다. 처음부터 붙어 있던 명칭 ‘비즈니스’ 덕분에 많은 오해가 있어 왔던 과학사업화에 대한 기본 정신을 살펴 보고자 한다. ‘기초과학연구원(Basic Science Institute, BSI)’은 우수한 연구자들을 모으고, 이들을 보호하고 지원하는 경영의 원칙과 그 시스템의 관리방안에 대해 언급하고자 한다.         <Invited Lectures> 권재훈  Jae-Hoon Kwon   서울시립대학교 수학과 교수  Professor, Department of Mathematics, University of Seoul 2011년도 대한수학회상 논문상 수상자 The winner of 2011 Excellent Research Paper Award   [Invited Lecture]  Algebra 13:40~14:20, October 21(Fri), 2011   Title : A combinatorial character formula for infinite dimensional representations of Lie algebras We give a combinatorial model for irreducible characters of various classes of Lie superalgebras, which form a Howe dual pair with a general linear Lie algebra of finite rank. The irreducible characters are realized in terms of certain Young bitableaux of skew shapes. These bitableaux can be viewed as a dual notion of Stembridge's rational tableaux for $\mathfrak{gl}_n$, and they have natural analogues of the Littlewood-Richardson rule and Knuth correspondence in classical Young tableaux.     노세은 Se Eun Noh   타이완 중앙연구원 수학연구소 연구원  Post-Doctor, Institute of Mathematics, Academia Sinica (Taiwan) 2010년도 대한수학회 상산 젊은수학자상 수상자  The winner of 2010 Sangsan Prize for young mathematicians   [Invited Lecture]  Analysis 13:40~14:20, October 21(Fri), 2011   Title : The Green’s function of the Navier-Stokes equations in $\mathbb R^3$ In this talk, we study the pointwise estimate of Green's function to the isentropic Navier-Stokes equations for compressible fluid in three dimension. Singular waves in the Green's function dominates short time behaviors. Low frequency waves represent large time behavior which shows dissipation and generalized Huygens' principle.     Michael G Roeckner   Professor, Department of Mathematics, Universität Bielefeld (Germany) Professor, Department of Statistics, Purdue University (USA)   [Invited Lecture]  Analysis & Applied Mathematics & Probability and Statistics 14:30~15:10, October 21(Fri), 2011   Title : Regularization of Ordinary and Partial Differential Equations by Noise It is a well-known phenomenon that an ordinary differential equation becomes "more regular", if one adds a noise term, as e.g. a stochastic differential given by a Brownian motion. On the level of the associated Fokker-Planck-Kolmogorov equations (FPKE), whose solutions are just the transition probabilities of the resulting solution process, this becomes more or less obvious, since the FPKE becomes elliptic, if the noise is not degenerate. From a purely analytic point of view, this regularizing property of the noise is most impressively manifested by the fact that noise can "produce" (existence and, in particular) uniqueness of solutions. Indeed, e.g. a classical result of A. Yu. Veretennikov (see [1] and the references therein), tells us that, given an initial condition, any two corresponding solutions of an ordinary differential equation in d-dimensional Euclidean space given by a just measurable bounded vector field and perturbed by the differential of a d-dimensional Brownian path, coincide for almost every such path. In contrast to this, in the deterministic case, neither existence nor uniqueness of solutions hold in such a case.   The purpose of this talk is to present recent results of the same type, but for partial differential equations perturbed by noise, i.e. for the infinite dimensional analogue of the situation described above.     Shoichi Fujimori   Professor, Department of Mathematics, Okayama University (Japan)   [Invited Lecture]  Geometry 13:40~14:20, October 21(Fri), 2011   Title : Maximal surfaces with singularities in the Lorentz-Minkowski 3-space Maximal surfaces in the Lorentz-Minkowski 3-space are the spacelike immersions with vanishing mean curvature. Like minimal surfaces in Euclidean 3-space, maximal surfaces admit the Weierstrass-type representation. Although a complete maximal immersion in the Lorentz-Minkowski 3-space is necessarily a spacelike plane, complete maximal surfaces with certain kinds of singularities have given arise to an interesting theory. In this talk, we shall survey the theory of maximal surfaces with singularities, and shall introduce several new examples.     Juan de Dios Perez   Director, Department of Geometría y Topología, University of Granada (Spain)   [Invited Lecture]  Geometry 14:30~15:10, October 21(Fri), 2011   Title : Jacobi operators on real hypersurfaces in complex two-plane Grassmannians Let $M$ be a real hypersurface of a complex two-plane Grassmannian $G_2 (\mathbb{C}^{m+2})$. This ambient space consists of all complex 2-dimensional linear subspaces in $\mathbb{C}^{m+2}$ and is equipped with both a Kaehler structure $J$ and a quaternionic Kaehler structure ${\mathfrak J}$ not containing $J$. These structures induced on $M$ both an almost contact metric structure $(\phi, \xi, \eta, g)$ and almost 3-contact metric structure $(\phi_{\nu}, \xi_{\nu}, \eta_{\nu}, g)$, $\nu =1,2,3$. Looking at that last structure we can consider on $M$ the distribution $\mathcal{D}^{\bot}$ spanned by $\{\xi_{\nu}\}$, $\nu =1,2,3$ and its orthogonal complementary distribution $\mathcal {D}$. The Jacobi operator $R_X$ with respect to a unit vector field $X$ on $M$ is defined as $R_X = R(\,\cdot\, ,X)X$, where $R$ denotes the Riemannian curvature tensor on $M$. Thus $R_X$ is a self-adjoint endomorphism of the tangent space and it is related to Jacobi vector fields on $M$ that are solutions of the well-known Jacobi equation. Thus on $M$ we have the structure Jacobi operator $R_{\xi}$ and the Jacobi operators $R_{\xi_{\nu}}$, $\nu =1,2,3$ corresponding to a basis of $\mathcal {D}^{\bot}$. Non-existence of real hypersurfaces in $G_2 (\mathbb{C}^{m+2})$ with parallel structure Jacobi operator were obtained by Jeong, Perez and Suh. Here we present a weaker result about the $\mathcal {D}^{\bot}$-parallelism of $R_{\xi}$ and characterize the tubes around totally geodesic $G_2 (\mathbb{C}^{m+1})$ in $G_2 (\mathbb{C}^{m+2})$ as the unique real hypersurfaces whose structure Jacobi operator is $\xi$-invariant (that is, its Lie derivative in the direction of $\xi$ vanishes). We also present similar results for Jacobi operators $R_{\xi_{\nu}}$, $\nu =1,2,3$, corresponding to a basis of $\mathcal {D}^{\bot}$.     김태희 Taehee Kim   건국대학교 수학과 교수  Professor, Department of Mathematics, Konkuk University   [Invited Lecture]  Topology 11:30~12:10, October 21(Fri), 2011   Title : Twisted Alexander polynomials and character varieties of knots It is known that twisted Alexander polynomials of a knot associated to finite representations detect fiberedness of the knot. On the other hand, it is still unanswered if twisted Alexander polynomials associated to SL(2,C)-representations of the knot group detect fiberedness of the knot. In this talk, we address the question from the view point of the character variety of the knot group. In particular, we show that if a nonfibered knot is alternating and small (e.g. nonfibered 2-bridge knot) then the character variety of the knot group has a curve component which contains only finitely many characters whose associated twisted Alexander polynomials are monic. We also discuss related problems such as duality of tiwsted Alexander polynomials and detecting knot genus. This talk is based on joint work with Stefan Friedl, Takayuki Morifuji and Takahiro Kitayama.     권오남 Oh Nam Kwon   서울대학교 수학교육과 교수  Professor, Department of Mathematics Education, Seoul National University   [Invited Lecture]  Mathematical Education 13:40~14:20, October 21(Fri), 2011   Title : Why the professor must be a stimulating teacher: Toward a new paradigm of teaching mathematics at university level The international phenomenon of expansion of the higher education sector had resulted in greater diversity in the intake of students. No loner is higher education the domain of the elite, but now more students ac access it that in any previous times. The differing backgrounds of students entering tertiary mathematics have a significant impact on the teaching and content that can be delivered.  The aim of this talk is to share some critical thoughts and to point out some constructive ideas on the educational goals of teaching mathematics at the university level.     Jiang Zeng   Professor, Département Mathématiques, Université Claude Bernard Lyon-I (France)   [Invited Lecture]  Mathematics for Information Sciences 11:30~12:10, October 21(Fri), 2011   Title : Separation variables and linearization coeffi cients of orthogonal polynomials We propose a new approach to the combinatorial interpretations of linearization coefficient problem. We first establish a difference system and then solve it combinatorially and analytically using the method of separation variables. We illustrate our approach by applying it to determine the number perfect matchings, derangements, and other weighted permutation problems.     천정희 Jung Hee Cheon   서울대학교 수리과학부 교수  Professor, Department of Mathematics, Seoul National University 2011년도 대한수학회상 논문상 수상자 The winner of 2011 Excellent Research Paper Award   [Invited Lecture]  Cryptography 11:30~12:10, October 21(Fri), 2011   Title : Recent problems in cryptography In this talk, we will introduce several recent problems in cryptography and discuss their possible approaches. One interesting topic is homomorphic encryptions and their applications in cloud computing security. We give some comparison among three-types of homormorphic encryptions based on lattice, bilinear group, and integer factorization, and introduce relevant problems. We also will deal with hard problems in lattice based cryptography as well as traditional Discrete Logarithm or Integer Factorization problem.