Date/Time : 14 May 2026 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Feiyue Huang, Beijing Normal University

In the study of blocks of Ariki–Koike algebras, the Uglov map—the essential link connecting multipartitions to partitions—originates from Frenkel’s level-rank duality of type $A^{(1)}$ affine Lie algebras on Fock space. Inspired by this result, we develop an analogous framework for each classical affine type once the corresponding level-rank duality is established. In this talk, we construct appropriate Fock spaces for all classical affine Lie algebras and introduce the associated combinatorial models, specifically Maya diagrams and abaci. By analyzing the action of the Virasoro algebra, we completely characterize the joint highest weight vectors in the Fock space, thereby formulating the corresponding level-rank duality theory. Using this new theory, we generalize the results of Fayers, Jacon-Lecouvey and Li-Qi et al. on block invariants of Ariki–Koike algebras, and provide combinatorial models for block invariants of cyclotomic KLR algebras for each classical affine type. This talk is based on a joint work with Wei Hu, Yanbo Li and Xiangyu Qi.

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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 : 07 May 2026 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Colin Piernot, EPFL

I will talk about the work (joint with Kexing Ying, EPFL) https://arxiv.org/abs/2604.08623, where we study the large-scale behavior of solutions to the Allen-Cahn reaction-diffusion equation with short range Gaussian initial data in dimension more than 3. Under diffusive rescaling, the non-linearity formally vanishes on large scales in this case. Accordingly, we prove a central limit theorem for the rescaled solution, more precisely, that it converges to the solution of the heat equation started from a white noise. The initial conditions for the limit depend non-trivially both on the source of randomness and on the non-linearity.

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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 : 05 May 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Nguyen Thac Dung, Hanoi University of Sciences, (VNU)

It is well-known that the Bochner technique is very useful to study geometry and topology of Riemannian manifolds. In this talk, I mention a new theory about curvature conditions related to the Bochner techniques following recent works by Petersen and Wink. I also introduce their applications on compact manifolds. Then, I will extend their results on non-compact complete Riemannian manifolds and prove some vanishing and rigidity results.

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Date/Time : 04 May 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Thomas Bitoun, Shanghai Institute for Mathematics and Interdisciplinary Sciences

Let Z be the germ of a complex hypersurface isolated singularity of equation f. We consider the family of analytic D-modules generated by the powers of 1/f and relate it to the pole order filtration on the de Rham cohomology of the complement of {f=0}. This work revisits Vilonen’s characterization of the intersection homology D-module.

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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 : 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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