This is the website of the Math Seminar at the Department of Mathematics Education, Seoul National University.
Title: Evolutionary coding based AI agents for mathematics
Abstract: The rectilinear crossing number is the minimum number of edge crossings in a straight-line drawing of a graph in the plane. Despite its elementary definition, even the case of complete graphs remains poorly understood, and progress over the past several decades has relied on a blend of geometric intuition, combinatorial reasoning, and increasingly sophisticated computational methods. In this talk, I will present a progress report on an attempt to use artificial intelligence as a new exploratory tool for this classical problem. After briefly surveying the history of the rectilinear crossing number and its known constructions, I will introduce OpenEvolve, an open-source framework inspired by AlphaEvolve, which has recently been applied to the study of mathematical conjectures. I will describe the framework at a high level and explain how it can be adapted to the rectilinear crossing number. I will then discuss results from this ongoing work. OpenEvolve was able to not only rediscover known optimal constructions for small complete graphs, but also improve upon a best known construction for a larger instance. I conclude by reflecting on the potential role of AI-assisted exploration in mathematics.
Venue: Room 103, Building 10-1 (Map), Seoul National University
Host: Boram Park
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Title: Fundamental PDEs
Abstract: Partial differential equations (PDEs) form a fundamental mathematical language for describing nature, from electrostatics and heat diffusion to wave propagation and fluid motion. In this talk, we revisit three basic examples---the Poisson, heat, and wave equations---and discuss why they are central to both mathematics and physics. We begin with the physical principles from which these equations arise, including conservation laws and Maxwell's equations, and then turn to some of the main analytical ideas used to study them. These include fundamental solutions, Fourier analysis, and energy methods, all of which provide insight into the qualitative behavior of solutions. Along the way, we highlight characteristic features of each equation: equilibrium and harmonicity for the Poisson equation, diffusion and smoothing for the heat equation, and propagation for the wave equation. More broadly, these examples illustrate several recurring themes in PDE: averaging principles, maximum principles, and rigidity phenomena such as Liouville-type theorems. They also reveal natural connections with other parts of mathematics, including complex analysis. The goal of the talk is to present an accessible introduction to some of the ideas that make these equations truly fundamental.
Venue: Room 207, Buiding 10, Seoul National University
Host: Jinmyoung Seok
Speaker: Cheolwon Heo (SUNY Korea), Kang-ju Lee (SNU), Minho Cho (KIAS)
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Venue: Room 207, Building 10 (Map), Seoul National University
Host: Boram Park