The MathNet Korea
Information Center for Mathematical Science

### 세미나

Information Center for Mathematical Science

#### 세미나

##### KAIST 응용수학세미나

After a short introduction of classification of computational technologies, I explain what Monte Carlo methods are and what advantages they have. I give overall perspectives of parallel random number generators, which play a crucial role in Monte Carlo methods. Later, I give some examples of Monte Carlo methods. I present how to solve some of elliptic partial differential equations such as Laplace, Poisson and linearized Poisson Boltzmann equation, and how to calculate permeabilities of idealized porours media, cube capacitance and mutual capacitance.

##### KAIST 응용수학세미나

Recently in last a decade, martingale representation got new attention because of its financial application. We study properties of L2 martingale spaces- orthogonality, stable subspaces, predictable representation property. We also study some applications and examples

##### KAIST 수리과학과 세미나

a cube has F=6 faces, E=12 edges and V=8 vertices. A pyramid with a square base has F=5 faces, E=8 edges and V=5 vertices. Euler discovered in 1750 that for these two cases, or for any other polyhedron, F-E+V=2. He published the result, but he confessed that he was not able to prove it! He found a proof one year later.

##### KAIST COMBINATORICS SEMINAR

The tableaux in the title, also known as permutation tableaux, are a recent combinatorial object that appeared in algebraic geometry, and was later connected to permutation statistics, and to the stationary distribution of a satistical mechanics model. We will present here a simple recursive decomposition of alternative tableaux. This translates into generating function enumerations of tableaux according to various statistics, and the decomposition is also used to determine bijections of the tableaux with certain families of trees, and with integer permutations.

##### KAIST COMBINATORICS SEMINAR
• Title : TBA
• Speaker : Hyeong-Kwan Ju
• Data : 2009-02-04 17:00:00
• Host : KAIST 수리과학과
• Place : Republic of Korea

##### KAIST COMBINATORICS SEMINAR

A clique of a graph is a set of pairwise adjacent vertices. We are interested in the maximum possible number of cliques in a graph. In general a graph with n vertices can have at most 2n cliques obviously. We will show that if we restrict to a graph with no Kr- minor, then such a graph can have at most O(n) cliques. Indeed this result is not new; several researchers already discovered the same bound. Previous best bound was 2crplog rn. We improved this to 2c log log rn. We also looked at other classes of graphs. As a corollary, we obtained a hypergraph generalization of the theorem of Thomason and Kostochka (independently) on the maximum number of edges in a graph with no Kr minor. This talk is based on a joint work with Fedor Fomin and Dimitrios Thilikos for relating tree-width and rank- width for planar graphs.

##### KAIST COMBINATORICS SEMINAR
• Title : TBA
• Speaker : Suyoung Choi
• Data : 2009-02-04 15:00:00
• Host : KAIST 수리과학과
• Place : Republic of Korea

##### KAIST COMBINATORICS SEMINAR

We first show that a certain n-dimensional polytope can be dissected into elementary polytopes of volume 1/n!. These elementary polytopes are indexed by certain labeled paths, which are in bijection with matchings of [1, 2n], i.e. involutions with no fixed points. We can thus find combinatorially the volume of the original poly-tope. Moreover, by specializing the bijection between paths and matchings, we can enumerate bijectively a certain class of permutations.

##### KIAS Seminar

Let X be a curve of genus at least 3, and U the moduli space of semistable vector bundles of rank r and slope g-1 over X. The variety U has a natural divisor whose support consists of bundles with nonzero sections. We give a geometric description of the tangent cone to this divisor at a stable point, which generalises the Riemann-Kempf singularity theorem for line bundles of degree g-1 over X. As a corollary, we give a generalisation of the geometric Riemann-Roch theorem to bundles of arbitrary rank.