[Notice] 2nd KMGS on Nov. 25, 2021

Our second KMGS will be held on November 25 via Zoom and Gather Town. The abstracts of two talks, by Wooyoung Chin and Donggyu Kim, are as follows.

1st slot (PM 12:00~12:20)
Speaker: Wooyoung Chin (진우영) from KAIST
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 KAIST & IBS
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)

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