Tuesday, November 5, 2024

2024-11-08 / 11:00 ~ 12:00

by Gwanghyun Jo()

Virtual element method (VEM) is a generalization of the finite element method to general polygonal (or polyhedral) meshes. The term ‘virtual’ reflects that no explicit form of the shape function is required. The discrete space on each element is implicitly defined by the solution of certain boundary value problem. As a result, the basis functions include non-polynomials whose explicit evaluations are not available. In implementation, these basis functions are projected to polynomial spaces. In this talk, we briefly introduce the basic concepts of VEM. Next, we introduce mixed virtual volume methods (MVVM) for elliptic problems. MVVM is formulated by multiplying judiciously chosen test functions to mixed form of elliptic equations. We show that MVVM can be converted to SPD system for the pressure variable. Once the primary variable is obtained, the Darcy velocity can be computed locally on each element.

2024-11-11 / 16:00 ~ 17:00

편미분방정식 통합연구실 세미나 - 편미분방정식:

by 이영애()

In this talk, we consider the self-dual O(3) Maxwell–Chern–Simons-Higgs equation, a semilinear elliptic system, defined on a flat two torus. We discuss about pointwise convergence behavior, which represents the Chern-Simons limit behavior of our system. Building upon this observation, we study the existence, stability, and asymptomatic behavior of solutions.

2024-11-05 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Monadic stability and monadic dependence

by Michał Pilipczuk(Institute of Informatics, University of Warsaw)

We will give an overview of the recent attempts of building a structure theory for graphs centered around First-Order transductions: a notion of containment inspired by finite model theory. Particularly, we will speak about the notions of monadic dependence and monadic stability, their combinatorial characterizations, and the developments on the algorithmic front.

2024-11-12 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Ehrhart theory revisited: Algebraic aspects, unimodality and more

by Karim Adiprasito(Jussieu Institute of Mathematics, Paris Rive Gauch)

Ehrhart theory is the study of lattice polytopes, specifically aimed at understanding how many lattice points are inside dilates of a given lattice polytope, and the study has a wide range of connections ranging from coloring graphs to mirror symmetry and representation theory. Recently, we introduced new algebraic tools to understand this theory, and resolve some classical conjectures. I will explain the combinatorial underpinnings behind two of the key techniques: Parseval identities for semigroup algebras, and the character algebra of a semigroup.

2024-11-07 / 11:50 ~ 12:40

대학원생 세미나 - 대학원생 세미나:

by 김준석()

TBA

2024-11-05 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

by 홍영준(KAIST)

This lecture explores the mathematical foundations underlying neural network approximation, focusing on the development of rigorous theories that explain how and why neural networks approximate functions effectively. We talk about key topics such as error estimation, convergence analysis, and the role of activation functions in enhancing network performance. Additionally, the lecture will demonstrate convergence analysis in the context of scientific machine learning, further bridging the gap between empirical success and theoretical understanding. Our goal is to provide deeper insights into the mechanisms driving neural network efficiency, reliability, and their applications in scientific computing.

2024-11-07 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by 변성수(서울대학교 수리과학부)

In this talk, I will discuss the expansion of the free energy of two-dimensional Coulomb gases as the size of the system increases. This expansion plays a central role in proving the law of large numbers and central limit theorems. In particular, I will explain how potential theoretic, topological, and conformal geometric information of the model arises in this expansion and present recent developments.

Events for the 취소된 행사 포함