Tuesday, August 13, 2024

2024-08-14 / 15:00 ~ 16:00

SAARC 세미나 - SAARC 세미나:

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In this talk, we first review nonlinear elliptic equations when the right-hand side is a finite measure. We discuss global gradient estimates of a solution for such measure data problems in bounded nonsmooth domains. We provide proper solutions and conditions which guarantee the regularity results. If time permits, we will consider parabolic problems with measure data.

2024-08-14 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 정수론:

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As part of the Langlands conjecture, it is predicted that every $\ell$-adic Galois representation attached to an algebraic cuspidal automorphic representation of $\mathrm{GL}_n$ over a number field is irreducible. In this talk, we will prove that a type $A_1$ Galois representation attached to a regular algebraic (polarized) cuspidal automorphic representation of $\mathrm{GL}_n$ over a totally real field $K$ is irreducible for all $\ell$, subject to some mild conditions. We will also prove that the attached Galois representation is residually irreducible for almost all $\ell$. Moreover, if $K=\mathbb Q$, we will prove that the attached Galois representation can be constructed from two-dimensional modular Galois representations up to twist. This is a joint work with Professor Chun-Yin Hui.

2024-08-13 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Formalizing matroid theory in a proof assistant

by Peter Nelson(University of Waterloo)

For the past few years, I’ve been working on formalizing proofs in matroid theory using the Lean proof assistant. This has led me to many interesting and unexpected places. I’ll talk about what formalization looks like in practice from the perspective of a combinatorialist.

2024-08-14 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 위상수학 세미나:

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Let S be a simply-connected rational homology complex projective plane with quotient singularities. The algebraic Montgomery-Yang problem conjectures that the number of singular points of S is at most three. In this talk, we leverage results from the study of smooth 4-manifolds, such as the Donaldson diagonalization theorem, to establish additional conditions for S. As a result, we eliminate the possibility of a rational homology complex projective plane of specific types with four singularities. We also identify infinite families of singularities that satisfy properties in algebraic geometry, including the orbifold BMY inequality, but are obstructed from being a rational homology complex projective plane due to smooth conditions. Additionally, we discuss experimental results related to this problem. This is joint work with Jongil Park and Kyungbae Park.

Events for the 취소된 행사 포함