2019 Fall Semester

[2019 Fall Semester]

매주 월요일 12:00

운영위원 : 권혜민 ( khmin1121@gmail.com , 팔달관 622호 )

감독위원 : 문지연 ( j9746@ajou.ac.kr , 팔달관 622호 )  

1. 9/16  (발표자 : 장현태) 

Title  :  Lower bound of the number of seed polytopes of picard number 4

Abstract :  We study the number of PL-spheres with a few vertices. The Picard number of PL-sphere of dimension n-1 with m vertices is defined as m-n. It is known that all PL-spheres of Picard number 3 are polytopal [Mani], and the number is known. Nevertheless, only little is known PL-spheres of Picard number 4. We focus on PL-sphers of Picard number 4. There are 5 and 39 PL-spheres of dimension 2 and 3, respectively. In this talk, we show that there are at least 337 PL-spheres of dimension 4 with 9 vertices.

2. 9/23  (발표자 : 권혜민) 

Title  : Introduction to combinatorial nullstellensatz

Abstract :  The Combinatorial Nullstellensatz is a theorem about the roots of a polynomial. It can be used in a list coloring of graph with graph polynomial. A coefficient of monomials in expansion of graph polynomial is related with orientations of graph. This seminar introduces the Combinatorial Nullstellensatz with graph polynomial and how to use it in list coloring with several examples.

3. 10/7  (발표자 : 윤영한) 

Title  : Brauer Algebras and Brauer Groups

Abstract :  In this talk, we define Brauer algebras, and Brauer group. Also we study relation of Severi-Brauer variaties between Brauer groups. 

4. 11/4  (발표자 : 이한경) 

Title  : COMSOL Multiphysics를 이용한 지하매설물 탐사

Abstract :  30년 전 단기간 대량의 인프라 건설로 현재 대도시 위주로 지반 함몰이 일어나고 있다. 따라서 이와 관련된 지하매설물의 보강이 필요한데 관련 기술의 한계와 문제점 때문에 어려움이 있는 상황이다. 따라서 이러한 문제를 현재 사용하고 있는 전기 비저항 기술을 이용하여 다양한 데이터를 이용하여 기계학습 후 전에 있던 전기 비저항 기술의 문제인 수학적 복잡성과 다수의 매설물을 판별하기 어려운 문제를 보완하려고 한다. 

5. 11/11  (발표자 : 장은진) 

Title  : Introduction of Grassmannians

Abstract : 주어진 field K에 대해 (n-1)-dim projective space는 n-dim v.s.over K에서 1-dim subspace들의 집합이다. 이때 Grassmannian(G(k,n))은 n보다 작은 k에 대해 k-dim subspace들의 집합들로 정의가 되된다. 이것을 Plücker embedding을 통해 (nCk-1)-dim projective space안에서 projective variety가 되는 것을 보인다. 

6. 11/25  (발표자 : 선종욱) 

Title  : Pointwise convergence, uniform convergence and Dini theorem

Abstract : Dini's theorem is one of the useful theorems for showing the difference between pointwise convergence and uniform convergence. When excluding at least one condition for the conclusion of Dini's theorem, we can find some examples readily which do not satisfy the uniform convergence(the conclusion of Dini's Theorem). Furthermore, this theorem has some applications and connections with Measure theory for graduate students' study. 

7. 12/2  (발표자 : 서형준) 

Title  : A study on defective coloring

Abstract :  A (k,d)-defective coloring of a graph is a k-coloring such that each color class induces a graph with maximum degree at most d.

We give a summary on some recent results of defective coloring. Especially, we give a proof of a result by Cowen, Cowen, and Woodall (1986), which states that a planar graph has a (3,2)-defective coloring.