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 : 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 #04-06 (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 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 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 : 21 Apr 2026 12:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Ulrich Horst, Humboldt University, Berlin

We establish a simple microstructure foundation for rough log-normal volatility models such as the rough Bergomi model. Unlike in earlier microstructure model we do not assume that that market orders arrive according to a heavy-tailed Hawkes process. Instead, we assume that orders arrive according to a standard Poisson process but have long lasting impact on asset price volatility. After suitable scaling the logarithmic volatility converges weakly to fractional Brownian motion mit H<1/2. Weak convergence rates are also established. The talk is based on joint work with Paul Hager, Thomas Wagenhofer and Wei Xu.

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Date/Time : 17 Apr 2026 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Joven Jia Xuan Teo, National University of Singapore

The nilpotent orbits of a Lie algebra are important objects relevant to representation theory, for instance in the definition of wavefront sets. If the algebra in question is one arising from a nondegenerate symmetric, symplectic, or Hermitian space over a topological field, it is known that the nilpotent orbits can be parametrised by objects called admissible labelled partitions. Furthermore, one can define in a reasonably simple way a partial ordering of these partitions that conjecturally corresponds to the closure ordering of the nilpotent orbits.

In this talk, we will introduce these admissible labelled partitions and the partial ordering defined on them. We then summarise the ideas in Djokovic’s proof of the real case. Finally, we discuss the obstacles in attempting to generalise these ideas to the p-adic case and beyond.

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