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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Date/Time : 20 Mar 2026 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Lucas Mason-Brown, University of Texas at Austin

Let G be a reductive group defined over a local field F. The local Langlands conjecture suggests a correspondence between (certain) infinite-dimensional irreducible G(F)-representations and (certain) finite-dimensional representations of the absolute Galois group \Gamma_F of F. If E/F is a field extension, then there is an inclusion \Gamma_F \subset \Gamma_E, and hence a natural map (restriction) from \Gamma_E-representations to \Gamma_F-representations. Composing with the (conjectural) Langlands correspondences for G(E) and G(F), we obtain a (conjectural) map, called `base change’ from G(F)-representations to G(E)-representations. In this talk, I will consider the special case when E=C and F=R. For real and complex groups, the local Langlands conjecture is a theorem (at least on the level of K groups), so there is a well-defined base change map from G(R)-representations to G(C)-representations (at least on the level of K groups). An interesting problem is to describe this correspondence directly, i.e. without appealing to the Langlands classification. I will describe a *partial* solution to this problem, following work of Clozel. Time permitting, I will formulate some conjectures regarding preservation of unitarity. This is joint work in progress with Andrei Ionov and David Nadler.

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Date/Time : 13 Mar 2026 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Leong Jin Ming, National University of Singapore

The Theta correspondence and Springer correspondence are important tools in representation theory, each having a different flavour. During the Relative Langlands conference in January, Zhiwei Yun gave a talk on his recent paper with Jiajun Ma, Congling Qiu, and Jialiang Zou in which they managed to reduce Theta correspondence to Springer correspondence. I will introduce the correspondences, give a brief summary of their findings, and then explain a conjectural manifestation of relative Langlands duality between Theta and Gan-Gross-Prasad via Springer theory.

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Date/Time : 30 Jan 2026 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Robin van Haastrecht, The University of Gothenburg

We study degenerate principal series representations of the split real group $G_{2(2)}$ induced from a character of a maximal parabolic subgroup whose unipotent radical is a Heisenberg group. Using the Lie algebra action on the space of $K$-finite vectors, we find the points of reducibility and the complementary series. The minimal representation and a limit of discrete series are identified as kernel of the corresponding Knapp–Stein intertwining operator. Moreover, we show that some quaternionic discrete series representations occur as the subrepresentation on which the intertwining operator vanishes of order $2$.

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