Our second KMGS will be held on November 25th, Thursday, via Zoom and Gather Town.

We invite Wooyoung Chin from Dept. of Mathematical Sciences, KAIST and Donggyu Kim from Dept. of Mathematical Sciences, KAIST and IBS Discrete Mathematics Group (DIMAG).

The abstracts of two talks are as follows.

1st slot (PM 12:00~12:20)

Speaker: Wooyoung Chin (진우영) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Paul Jung (폴 정 교수님)

Title: A new elementary proof of the central limit theorem

Discipline: Probability

Abstract: The proof of the central limit theorem (CLT) is often deferred to a graduate course in probability because the notion of characteristic functions is sometimes considered too advanced. I’ll start the talk by reviewing the past efforts to provide an elementary proof of the CLT which is not based on characteristic functions. Then I will explain a new proof of the CLT that derives it from the de Moivre-Laplace theorem, which is the CLT for Bernoulli random variables. The de Moivre-Laplace theorem is the first instance of the CLT in the history, and can be proved directly by computation.

Language: Korean (English if it is requested)

2nd slot (PM: 12:25~12:45)

Speaker: Donggyu Kim (김동규) from Dept. of Mathematical Sciences, KAIST and IBS Discrete Mathematics Group (DIMAG), supervised by Prof. Sang-il Oum (엄상일 교수님)

Title: Eigenvalues and parity factors in graphs

Discipline: Graph Theory

Abstract: Let $G$ be a graph and let $g, f$ be nonnegative integer-valued functions defined on $V(G)$ such that $g(v) \le f(v)$ and $g(v) \equiv f(v) \pmod{2}$ for all $v \in V(G)$.A $(g,f)$-parity factor of $G$ is a spanning subgraph $H$ such that for each vertex $v \in V(G)$, $g(v) \le d_H(v) \le f(v)$ and $f(v)\equiv d_H(v) \pmod{2}$.In this paper, we prove sharp upper bounds for certain eigenvalues in an $h$-edge-connected graph $G$ with given minimum degree to guarantee the existence of a $(g,f)$-parity factor; we provide graphs showing that the bounds are optimal. This is a joint work with Suil O.

Language: Korean (English if it is requested)