Date/Time : 09 Sep 2026 13:30
Venue : S16 #05-18
Speaker : Toshihisa Kubo, Ryukoku University

Let X be a smooth manifold and Y a smooth submanifold of X. Let G’ ⊂ G be Lie groups, with G acting on X and G’ acting on Y. A differential operator D from the space of smooth sections of a G-equivariant vector bundle over X and to that of a G’-equivariant vector bundle over Y is called a differential symmetry breaking operator (DSBO for short) if D is G’-intertwining.

In general, the classification and construction of DSBOs are challenging problems. Around 2010, Toshiyuki Kobayashi introduced a fascinating idea for addressing these problems when both X and Y are flag manifolds. We refer to the resulting machinery as the F-method. The F-method reduces the classification and construction of DSBOs to solving a certain system of partial differential equations via the algebraic Fourier transform of generalized Verma modules. In this talk, we shall first discuss recent progress on the F-method. We shall then give explicit formulas for the DSBOs for (G,G’)=(GL(3,R), GL(2,R)) with minimal parabolic subgroups. This talk is based on joint work with Jonathan Ditlevsen and Víctor Pérez-Valdés.

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Date/Time : 19 Aug 2026 13:30
Venue : S16 #05-18
Speaker : Liron Speyer, Okinawa Institute of Science and Technology

I will give a brief account of the combinatorial representation theory of type A Iwahori–Hecke algebras, and their realisation as cyclotomic KLR algebras. In this story, I will largely focus on the decomposition number problem as one of the key problems in this field, and James’s conjecture, which drove a lot of research until Williamson showed it to be false in 2013. While Williamson’s counterexample is incredibly large, and beyond explicit computation, I recently discovered a new counterexample, which is of minimal size. I will explain this counterexample in the talk, as well as touching on how I found it.

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Date/Time : 12 Aug 2026 13:30
Venue : S16 #05-18
Speaker : Dinesh S. Thakur, University of Rochester

After reviewing some basic facts of classical diophantine approximation, diophantine equations, we will discuss various analogs, contrasts, tools, and open questions in the finite characteristic situation.

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Date/Time : 27 Jul 2026 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Pavel Turek, Okinawa Institute of Science and Technology

A central open problem of the modular representation theory of symmetric groups (and Hecke algebras) is the computation of decomposition numbers, which describe irreducible constituents of Specht modules in prime characteristic. These numbers are organised in a block matrix, called the decomposition matrix, whose structure remains a mystery. In this talk, we present new whole columns of this matrix labelled by a novel family of partitions called d-balanced partitions; this seems to be the first description of whole columns in each block to date! Depending on the number d, we either get an algebraic interpretation (for d=2, this is joint with David Hemmer) or characteristic-free columns applicable to Hecke algebras (for d>2, this is joint with Bim Gustavsson, Stacey Law, Lorenzo Putignano and Liron Speyer).

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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 : 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 : 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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Date/Time : 27 Mar 2026 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Wu Xingyu, National University of Singapore

Let F be a local field and let G be a split exceptional group over F. The theta correspondence for the dual pair (SL2, G) relates irreducible representations of SL2(F) and G(F), and a basic problem is to determine which representations of G(F) occur in the lift and with what multiplicity. In this talk, based on Hanzer and Savin’s work, I will explain a multiplicity-one statement for an oscillator-type model attached to a fixed additive character, and how it leads to a classification of those irreducible representations of G(F) that appear as its quotients. As a consequence, one obtains a clean criterion: a representation of G(F) occurs precisely when it is the theta lift of a generic irreducible representation of SL2(F). I will sketch the main ideas behind this reduction and indicate how it guides the computation of the correspondence.

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