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 : 30 Apr 2026 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Han Fei, National University of Singapore

Spin geometry is one of major areas of differential geometry, centered on manifolds admitting spin and spin^c structures. String geometry may be viewed as its natural refinement: by requiring higher obstructions to vanish, new invariants, most notably modular invariants, emerge, motivated by infinite-dimensional refinements of the Atiyah–Singer index theory.

In this talk, I will present some of our recent work on the theory and applications of spin and string geometry. A closely related object is the loop space of a manifold, which provides a typical and natural example of infinite-dimensional geometric object. I will also discuss our development of geometric and cohomological structures on loop spaces and their applications to string dualities.

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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 : 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 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Cesar Cuenca, Ohio State University

Following a discussion of the continuous Gaussian beta ensemble and the classical Law of Large Numbers (LLN) for its empirical measures in the regimes of fixed and high temperature, we switch to the setting of discrete-space particle systems. By using Fourier transforms based on Jack symmetric polynomials, we study discrete N-particle ensembles in the regime where the inverse temperature parameter tends to zero, simultaneously as the number of particles in the system tends to infinity. We prove the LLN and characterize the limiting measure in terms of a moment problem. For fixed-time distributions of the discrete beta-Dyson Brownian motion, we calculate the densities of the limiting measures and express them in terms of the zeroes of certain entire functions and in terms of the eigenvalues of Jacobi operators. This talk is based on joint works with Florent Benaych-Georges, Vadim Gorin and Maciej Dolega.

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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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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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