Wednesday, August 14, 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.

2024-08-21 / 15:00 ~ 17:00

학과 세미나/콜로퀴엄 - 산업응용수학 세미나: 웨트로폴리스 홍수 예측에서의 극한 환경 이벤트와 극한 파도 역학

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An introduction and overview will be given of extreme events in Wetropolis flood investigator and of extreme water-wave motion in a novel wave-energy device. I will give an overview of the mathematical models and simulations of the phenomena seen in the following movies as well as related phenomena. Subsequently, mathematical and numerical aspects of the novel wave-energy device will be highlighted. As well as a discussion on the Wetropolis World proposal. The related movies which explain Wetropolis: Wetropolis-II (temp link) 2024: https://www.youtube.com/watch?v=g8znktYpxvY, Wetropolis-I 2022: https://www.youtube.com/watch?v=rNgEqWdafKk, The wave-energy device was motived by the bore-soliton-splash (2010): https://www.youtube.com/watch?v=YSXsXNX4zW0&list=FL6mc7mUa6M4Bo2VkD970urw, as well as a first proof of principle (2013): https://www.youtube.com/watch?v=SZhe_SOxBWo

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.

2024-08-21 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 확률론:

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In the first part of the talk, I will discuss the asymptotic expansions of the Euclidean Φ^4-measure in the low-temperature regime. Consequently, we derive limit theorems, specifically the law of large numbers and the central limit theorem for the Φ^4-measure in the low-temperature limit. In the second part of the talk, I will focus on the infinite volume limit of the focusing Φ^4-measure. Specifically, with appropriate scaling, the focusing Φ^4-measure exhibits Gaussian fluctuations around a scaled solitary wave, that is, the central limit theorem. This talk is based on joint works with Benjamin Gess, Pavlos Tsatsoulis, and Philippe Sosoe.

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.

2024-08-21 / 16:00 ~ 18:00

학과 세미나/콜로퀴엄 - 위상수학 세미나:

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In this talk, I will talk about isotopy problems of Seifert surfaces pushed in to the 4-ball. In particular, I will prove that every Seifert surface of a non-split alternating link become isotopic in the 4-ball. This is a joint work with Maggie Miller and Jaehoon Yoo.

Events for the 취소된 행사 포함