http://mathsci.kaist.ac.kr/~manifold/Arithmetics.html

We are considering a gas or "plasma" of electrons in a plane, in the presence of an external field which is strong enough near infinity that the particles be confined to a finite portion of it. If we let the number of particles increase indefinitely, the gas will condensate on a certain compact subset of the plane, known as the "droplet". The shape of this droplet depends on the external field. The problem to determine the details of it is the Laplacian growth problem from fluid mechanics. This is what gives the classical equilibrium distribution of the plasma. Looking at the gas in further detail, the first thing to observe is that the repulsion between the electrons will cause a "very uniform distribution" in the vicinity of the droplet. One of our theorems assert that the fluctuations about the equilibrium converges to a Gaussian field on the droplet with free boundary conditions. If there is time, I will also mention a new kind of field approximations which we can use to justify much of the physical formalism of conformal field theory. Joint work with Håkan Hedenmalm, Nikolai Makarov, and Nam-Guy Kang, in different constellations.

During the last decade, inverse combinatorial optimization problems have found an increased interest in the optimization community. Whereas an optimization problem asks for a feasible solution with minimum or maximum objective function value, inverse optimization problems are defined with a feasible solution, and aim to perturb as little as possible the parameters (costs, profits, etc.) of the problem so that the given solution becomes optimum in the new instance. In this talk, we introduce some generalized inverse combinatorial problems, and investigate inverse chromatic number problems in permutation graphs and interval graphs.

http://mathsci.kaist.ac.kr/~manifold/Arithmetics.html

We will define quasitoric orbifolds, describe their topological
invariants. We will discuss almost complex structures and blowdowns
on four dimensional quasitoric orbifolds and a McKay correspondence
for these.

We will discuss basic facts about differentiable orbifolds and
intorduce Chen-Ruan cohomology groups and Mckay correspondence.

Many interesting works on topological algebras are best understood in view of algebraic topology or diffrential geometry. Since Gelfand-Naimark's celebrated characterization of commutative C*-algebras as a dual of locally compact Hausdorff space, the category of non-commutative C*-algebras has been regarded as "non-commutative locally compact Hausdorff spaces". In this talk, he will introduce so called non-commutative (algebraic) topology and (differential) geometry relying on his own appreciations of the subjects. 

The notion of a matroid was introduced by H. Whitney in 1935 as an abstraction of “linear independence” in a vector space. In 1960’s, J. Edmonds found that matroids are closely related to an efficient algorithm. After then, many researchers have studied and extended Matroid Theory. In 2007, S. Fujishige, G. A. Koshevoy, and Y. Sano introduced cg-matroids as an generalization of matroids. They defined a matroid-like structure on an abstract convex geometry, where the notion of an abstract convex geometry was introduced by P. H. Edelman and R. E. Jamison in 1985. In this talk, I will introduce the theory of cg-matroids. In particular, I will talk about the definition and some examples of cg-matroids, some combinatorial properties and characterization of cg-matroids, and the relationship between cg-matroids and the greedy algorithm.

In this talk I will introduce to two topological objects, that are topological configuration spaces and discrete configuration spaces, and Discrete Morse theory, which is one of combinatorial versions of Morse theory. We will discuss relations between topological configuration space and discrete configuration spaces, and applications of Discrete Morse theory to studing discrete configuration spaces.

The only possible fibration on a K3 surface is an elliptic fibration, with base P^1. Lagrangian fibrations on holomorphic symplectic manifolds are higher-dimensional generalizations of elliptic K3 surfaces. In this talk I will describe some results about Lagrangian fibrations concerning their bases, discriminant loci, singular fibres, and classifying maps. 

Recent brain research relies heavily on connectionism since connection exists universally in the brain, for example, between neuron and neurons, between region and regions, between brains and cultures. To examine different levels of connection within brain, various neuroimaging techniques have been suggested to show functional brain connection. Anatomic connection is provided by diffusion tensor imaging and functional connection is dealt by functional MRI. These techniques have been used for diagnosis and exploration of diseases and also for understanding brain and interactions. In this presentation, we will review advanced methods for brain connectivity in the respect of anatomic connection, functional connection from neuronal level to social brain level.

세상 모든 건은 서로 연결되어 있다는 간단한 생각에서 출발한 복잡계에 대한 연구는 21C에 들어와 물리학의 중요한 주제로 떠오르고 있다. 복잡계연구에서는 여러 분야의 서로 다른 많은 수의 객체(노드)들 간의 복잡한 상요작용(링크)이 얽혀진 네트워크를 분석함으로써 복잡계의 구조의 성질 및 그 안에서 일어나는 여러 협동현상들을 이해하려 하고 있다. 이번 콜로퀴엄에서는 복잡계 네트워크 과학을 소개하고 IT분야 Google의 전략과 미래인터넷연구, 시스템생물학을 통한 신약개발 노력, 18대 국회의원의 네트워크 분석, 도로교통망의 체증해소 문제, 컴퓨터 바이러스와 AIDS 등의 전염병 확산방지대책등 최근의 복잡계 연구동향을 간략히(?) 살펴보고자 한다.

Matrix analogues of embedded surfaces, as well as discrete versions of curvature
and the Euler characteristic will be presented, and the new notions, related to a novel algebraic formulation
of classical differential geometry, will be illustrated by a large class of examples.

We shall construct infinitesimal deformations of a complex surface with boundary, which is the complement of a tubular neighborhood of a special linear chain of smooth rational curves. We show that the deformation induces a non-trivial deformation of the complex structure on some divisor on Y. 

  장 소 : 자연과학동(E6-1) #3433

 일 정 : 2010. 5. 3(월) 15:00~17:30

  1. 권오상 박사 (15:00~15:15)

    - Title : Existence of standing wave for Nonlinear Schrodinger equation

  2. 김정애 박사 (15:15~15:30)

   - Title : Nonlinear viscoelastic equation

  3. 신동화 박사 (15:30~15:45)
   - Title : Diophantine equations and modular forms

  4. 윤석배 박사 (15:45~16:00)

    - Title : An introduction to Kinetic equations

  5. 이완석 박사 (16:00~16:15)

    - Title : On the classification of non-normal del Pezzo varieties

  6. 임병화 박사 (16:15~16:30)

    - Title : Firm Size Growth Effect on the Risk-Taking Behavior: BSDE Approaches

  7. 장광성 박사 (16:30~16:45)

    - Title : Extraction immersed finite element method for Stokes flow with singular

               forces

  8. 정의진 박사 (16:45~17:00)

    - Title : Classification problems in symbolic dynamics

  9. 주항연 박사 (17:00~17:15)

    - Title : On Homoclinic points, Recurrences and Chain recurrences of volume-preserving

               diffeomorphisms without genericity

  10. Zribi, Habib 박사 (17:15~17:30)

    - Title : Small Perturbation of an Interface: Asymptotic Formulas and Reconstruction

             of Small Interface Changes