Formalizing mathematics: why it matters now

Now

현재 Formalizing mathematics: why it matters now

BK21 FOUR Rookies Pitch | 강연자 : 황병학 | 소속 : KIAS

Formalizing mathematics involves translating mathematical statements from natural language into a precise formal language that computers can interpret. As modern mathematics becomes deeper and more complex, the importance of formalization has grown significantly. In this talk, I will provide a brief introduction to the concept of formalization, discuss its significance, and explore how formalization and AI interact with each other.

Total domatic number of cubic graphs

BK21 FOUR Rookies Pitch | 강연자 : 권혜민 | 소속 : KIAS

The theory of dominating sets in graph theory has attracted considerable attention from numerous researchers, and various related notions and variations have been introduced. In this talk, we present the concepts of total dominating sets and the total domatic number. In particular, we discuss conditions under which a cubic graph has total domatic number at least 2.

학부생을 위한 ɛ 강연: A Zoo of Noncompact Surfaces

수학강연회 | 강연자 : 곽상훈 | 소속 : 서울대학교

학부 위상수학의 한 목표는 콤팩트한 곡면은 “구멍의 개수”로 완전히 분류됨을 소개하는 것입니다. 하지만 구멍이 무한히 많아지면 어떻게 될까요? 본 강연에서는 무한 곡면의 다양한 예를 살펴보고, Kerékjártó, Richards, Brown, Messer 등 다양한 수학자들이 제시한 무한 곡면에 대한 분류 정리들을 소개합니다.

Ancient solutions to the Yamabe flow

수학강연회 | 강연자 : 김승혁 | 소속 : 한양대학교

The Yamabe flow is a geometric evolution equation whose goal is to improve the geometry of a manifold by deforming its metric toward one with constant scalar curvature. In this talk, I will introduce the basic background and motivation for the Yamabe flow and then discuss recent developments concerning ancient solutions, namely, solutions that exist for all negative times. In the latter part of the talk, I will present joint work with Dr. Haixia Chen (Hanyang University) and Prof. Monica Musso (University of Bath, UK) on the existence of nonradial ancient solutions.

※ 동영상 5월 10일 공개 예정

Strichartz estimates for the Schrödinger equation on the two-dimensional torus

BK21 FOUR Rookies Pitch | 강연자 : 곽범종 | 소속 : KAIST

The study of estimating the size of a solution to a linear dispersive partial differential equation, called the Strichartz estimate, has been of interest in both partial differential equations and harmonic analysis.

In this talk, I will focus on Strichartz estimates for the Schrödinger equation on a flat two-dimensional torus, which has rich connection to discrete mathematics. I will briefly introduce some of the connections, ranging from number theory to, more recently, incidence geometry and additive combinatorics.

Dirichlet problem and regular boundary points for elliptic equations in non-divergence and double divergence form

BK21 FOUR Rookies Pitch | 강연자 : 김동하 | 소속 : 서울대학교 쎈 펠로우

In the theory of elliptic partial differential equations, the Dirichlet problem has long been a central topic. A fundamental question is to identify domains for which the Dirichlet problem is always solvable.Equivalently, this question leads to the characterization of regular boundary points, a classical problem in the theory of elliptic equations.. For the Laplace equation, this problem was completely solved by Wiener in 1924. He established the celebrated Wiener criterion, which characterizes regular boundary points in terms of a series of capacities. In this talk, we consider the Dirichlet problem for second-order elliptic equations in non-divergence form and double divergence form. We introduce a potential theory framework for these operators, including Perron’s method, capacity theory, and Wiener’s criterion. Assuming that the leading coefficients satisfy the Dini mean oscillation condition, we also establish the equivalence between regular boundary points for these operators and those for the Laplace operator.