Date/Time : 12 May 2026 14:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : LIU Jie, Chinese Academy of Sciences

I will report a joint work with Baohua Fu proving that most Hamiltonian reductions of cotangent bundles are affine closures of cotangent bundles, together with some applications.

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Date/Time : 05 May 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Yu-Sen An (Nanjing University of Aeronautics and Astronautics), Yu-Sen An (Nanjing University of Aeronautics and Astronautics)

With the detection of gravitational waves and the release of black hole shadow images, black hole becomes a real astrophysical object instead of a mere mathematical artifact. However, while extensive works have been done on the black hole exterior, the interior region remains far less explored. Thus in this talk, I will focus on the black hole interior structure, from the horizon down to the singularity. We are particularly interested in the black hole spacetime in anti–de Sitter (AdS) space since this can be connected to quantum many body systems through holographic duality. I will show that the interior dynamics are far richer than previously expected. I will choose several important holographic models such as holographic superconductor to illustrate these distinct behaviors. Finally, I will demonstrate how to connect these interior structures to the boundary physics, potentially revealing new aspects of holographic duality.

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Date/Time : 04 May 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Chung Pang Mok , Shanghai Institute for Mathematics and Interdisciplinary Sciences

In this talk we discuss the Birch and Swinnerton-Dyer formula modulo square of rational numbers for the quadratic twist family of a given elliptic curve over Q. In particular we show the following: let E be a semistable elliptic curve over Q with conductor N, whose analytic rank is at most one, then for any positive fundamental discriminant D that is relatively prime to N, such that the quadratic twist E^D again has analytic rank at most one, we have that the Birch and Swinnerton-Dyer formula modulo square of rational numbers holds for E if and only if it holds for E^D.

Joint work with Alexander Barrios.

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Date/Time : 29 Apr 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Heejong Lee, Korea Institute for Advanced Study (KIAS)

Given a Galois representation attached to a regular algebraic cuspidal automorphic representation, the Hodge–Tate weight of the Galois representation is matched with the weight of the automorphic representation. Serre weight conjectures are mod p analogue of such a correspondence, relating ramification at p of a mod p Galois representation and Serre weights of mod p algebraic automorphic forms. In this talk, I will discuss how to understand Serre weight conjectures and modularity lifting as a relationship between representation theory of finite groups of Lie type (e.g. GSp4(Fp)) and the geometry of p-adic local Galois representations. Then I will explain the proof idea in the case of GSp4. This is based on a joint work with Daniel Le and Bao V. Le Hung.

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Date/Time : 29 Apr 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Juncheng Wei, The Chinese University of Hong Kong

In 2023, one year before his death, H. Brezis posted 28 open questions which he described as “challenging and difficult”. In this talk I will give complete answer to the first open question—Problem 1.1 on Brezis-Nirenberg problem on three dimensional unit ball, and the seventh open question—Problem 3.1 on harmonic map equation on disk.

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Date/Time : 22 Apr 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Phan Quoc Vuong,

Blow-up of a graph is a useful trick in extremal graph theory, replacing every vertex with a finite collection of copies so that the copies of two vertices are adjacent if and only if the originals are. In this talk, I will explain how to extend the blow-up trick to general combinatorial objects, and discuss about its potential application, illustrated by a recent result related to hypergraph Turan problem.

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Date/Time : 22 Apr 2026 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Swee Hong Chan, Rutgers University

A sequence of nonnegative real numbers a_1, a_2,… , a_n, is log-concave if a_i^2 >= a_{i-1}a_{i+1} for all i ranging from 2 to n-1. Examples of log-concave inequalities range from inequalities that are readily provable, such as the binomial coefficients a_i = \binom{n}{i}, to intricate inequalities that have taken decades to resolve, such as the number of independent sets a_i in a matroid M with i elements (otherwise known as the first Mason’s conjecture; and was resolved by June Huh in 2010 in a remarkable breakthrough). It is then natural to ask if it can be shown that the latter type of inequalities is intrinsically more challenging than the former. In this talk, we provide a rigorous framework to answer this type of questions, by employing a combination of combinatorics, complexity theory, and geometry.

This is a joint work with Igor Pak.

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Date/Time : 22 Apr 2026 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Jia Shi, Indiana University Bloomington

In this talk, I will introduce the implosion blow-up results for the compressible Euler, the compressible Navier-Stokes equations, and the defocusing nonlinear Schrödinger equation. We will discuss the existence of self-similar solutions and the stability near those solutions. During the talk, I will mention our work with Gonzalo Cao-Labora, Javier Gómez-Serrano, and Gigliola Staffilani on the first non-radial implosion result for those three equations. If there is time, I will also mention our work on self-similar solutions of a hydrodynamic equation that may formally arise as potential blow-up profiles of the focusing NLS equation.

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Date/Time : 22 Apr 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Khakim Egamberganov, National University of Singapore

We study the long-time behaviour of vorticity in three-dimensional axisymmetric Euler flows without swirl. This equation is globally well-posed when the initial vorticity satisfies some integrability conditions, but due to the presence of vortex stretching term, the vorticity and related quantities tend to grow in time. In this talk, we will discuss some improved upper and lower bounds for vorticity growth. This talk is based on joint work with Yao Yao.

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