Tuesday, October 11, 2022

2022-10-18 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Uniform random expressions lack expressivity

by Florent Koechlin(LORIA, INRIA, Nancy, France)

In computer science, random expressions are commonly used to analyze algorithms, either to study their average complexity, or to generate benchmarks to test them experimentally. In general, these approaches only consider the expressions as purely syntactic trees, and completely ignore their semantics — i.e. the mathematical object represented by the expression. However, two different expressions can be equivalent (for example “0*(x+y)” and “0” represent the same expression, the null expression). Can these redundancies question the relevance of the analyses and tests that do not take into account the semantics of the expressions? I will present how the uniform distribution over syntactic expression becomes completely degenerate when we start taking into account their semantics, in a very simple but common case where there is an absorbing element. If time permits it, I will briefly explain why the BST distribution offers more hope. This is a joint work with Cyril Nicaud and Pablo Rotondo.

2022-10-14 / 17:00 ~ 18:00

SAARC 세미나 - SAARC 세미나:

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Wigner's jellium is a model for a gas of electrons. The model consists of unit negatively charged particles lying in a sea of neutralizing homogeneous positive charges spread out according to Lebesgue measure. The key challenge in analyzing this system stems from the long-range Coulomb interactions. While the motivation for the jellium stems from physics, Coulomb systems appear in a variety of different research fields such as random matrix theory. In the first part of this talk, I will review key limit results for classical Coulomb systems in large domains. In the second part, I will present some recent advances for quantum Coulomb systems.

2022-10-11 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Exact results for generalized extremal problems forbidding an even cycle

by Nika Salia(IBS 극단조합및확률그룹)

We determine the maximum number of copies of $K_{s,s}$ in a $C_{2s+2}$-free $n$-vertex graph for all integers $s \ge 2$ and sufficiently large $n$. Moreover, for $s\in\{2,3\}$ and any integer $n$ we obtain the maximum number of cycles of length $2s$ in an $n$-vertex $C_{2s+2}$-free bipartite graph. This is joint work with Ervin Győri (Renyi Institute), Zhen He (Tsinghua University), Zequn Lv (Tsinghua University), Casey Tompkins (Renyi Institute), Kitti Varga (Technical University of Budapest BME), and Xiutao Zhu (Nanjing University).

2022-10-13 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

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Order types are a combinatorial classification of finite point sets used in discrete and computational geometry. This talk will give an introduction to these objects and their analogue for the projective plane, with an emphasis on their symmetry groups. This is joint work with Emo Welzl: https://arxiv.org/abs/2003.08456

Events for the 취소된 행사 포함