Friday, November 1, 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.

2024-11-01 / 10:00 ~ 11:00

학과 세미나/콜로퀴엄 - 박사논문심사: 점근원뿔에 작용하는 군의 핵에 관한 연구

by 장원용(KAIST)

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.

2024-11-01 / 13:30 ~ 14:30

학과 세미나/콜로퀴엄 - Topology, Geometry, and Data Analysis:

by ()

The Gromov-Wasserstein (GW) distance is a generalization of the standard Wasserstein distance between two probability measures on a given ambient metric space. The GW distance assumes that these two probability measures might live on different ambient metric spaces and therefore implements an actual comparison of pairs of metric measure spaces. A metric-measure space is a triple (X,dX,muX) where (X,dX) is a metric space and muX is a fully supported Borel probability measure over X. In Machine Learning and Data Science applications, this distance is estimated either directly via gradient based optimization approaches, or through the computation of lower bounds which arise from distributional invariants of metric-measure spaces. One particular such invariant is the so-called ‘global distance distribution’ which precisely encodes the distribution of pairwise distances between points in a given metric measure space. This invariant has been used in many applications yet its classificatory power is not yet well understood. This talk will overview the construction of the GW distance, the stability of distributional invariants, and will also discuss some results regarding the injectivity of the global distribution of distances for smooth planar curves, hypersurfaces, and metric trees.

2024-11-01 / 10:00 ~ 12:00

SAARC 세미나 - SAARC 세미나:

by ()

The objective of the tutorial Computer-Assisted Proofs in Nonlinear Analysis is to introduce participants to fundamental concepts of a posteriori validation techniques. This mini-course will cover topics ranging from finite-dimensional problems, such as finding periodic orbits of maps, to infinite-dimensional problems, including solving the Cauchy problem, proving the existence of periodic orbits, and computing invariant manifolds of equilibria. Each session will last 2 hours: 1 hour of theory followed by 1 hour of hands-on practical applications. The practical exercises will focus on implementing on implementing computer-assisted proofs using the Julia programming language.

2024-11-01 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 기타: About birational classification of smooth projective surfaces I

by 김재홍(KAIST)

This is a reading seminar to be given by Mr. Jaehong Kim (a graduate student in the department) on foundations of the intersection theory and the classification theory of complex algebraic surfaces. He will give three 2-hour long talks.

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