Date/Time : 03 Oct 2025 14:00
Venue : S16 #04-35
Speaker : Song Linliang, Tongji University

In this talk, we introduce two new diagrammatic monoidal categories—the affine q-web category and the affine q-Schur category—along with their respective cyclotomic quotient categories. We construct diagrammatic integral bases for the Hom-spaces in all these categories. Furthermore, we establish the following isomorphisms, which provide the first diagrammatic presentations of these important algebras: (i) the path algebras of the affine q-web category are isomorphic to R. Green’s affine q-Schur algebras; (ii) the path algebras of the affine q-Schur category are isomorphic to Maksimau-Stroppel’s higher level affine q-Schur algebras; and most significantly, (iii) the path algebras of the cyclotomic q-Schur categories are isomorphic to Dipper–James–Mathas’ cyclotomic q-Schur algebras. This is based on joint projects with Yaolong Shen and Weiqiang Wang.

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Date/Time : 30 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Chong Jing Quan, National University of Singapore

In this talk we will introduce several operators on extended multi-segments that preserves the associated representations. Using those operators, we will classify the A-packets that contain a fixed representation. We will demonstrate the ideas of the proof using several examples.

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Date/Time : 24 Sep 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Shuichiro Takeda, The University of Osaka

Let V be a quadratic space over a nonarchimedean local field of characteristic 0. The orthogonal group O(V) and the special orthogonal group SO(V) have a unique nontrivial GL_1 -extension called GPin(V) and GSpin(V), respectively. Let W\subseteq V be a subspace of codimension 1. Then there are natural inclusions GPin(W)\subseteq
GPin(V) and GSpin(W)\subseteq GSpin(V). One can then consider the Gan-Gross-Prasad (GGP) periods for GPin and GSpin. In this talk, I will talk about the multiplicity-at-most-one theorem for the local GGP periods for GPin and GSpin. This is a joint work with Melissa Emory.

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Date/Time : 23 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Chong Jing Quan, National University of Singapore

For classical groups, the explicit construction of local Arthur packets in terms of enhanced Langlands parameter has been studied by a sequence of work of C. Mœglin, B. Xu and H. Atobe. In this talk, we will discuss Atobe’s algorithm for this construction. We will introduce the combinatorial object called extended multi-segments and their associated representations. If time permits, we will talk about several operators on extended multi-segments that preserves the associated representations.

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Date/Time : 16 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Lo Chi-Heng, National University of Singapore

Local Arthur packets consist of local components of automorphic representations. In the study of automorphic representations, it is often important to understand the properties of a local representation through the local Arthur packets to which it belongs. However, a local representation may lie in multiple local Arthur packets. This causes difficulty, but also provides extra structure for these kinds of problems. In this series of talks, we will discuss the intersection phenomenon for p-adic symplectic and special odd orthogonal groups. We will then explore several applications, including the closure ordering conjecture for local Arthur packets and Jiang’s conjecture on the upper bounds of wavefront sets (and more).

In the first talk, I will introduce the definition of local Arthur packets and their basic properties, and then sketch a geometric construction of local Arthur packets under certain assumptions

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Date/Time : 02 Sep 2025 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Yang Ruotao, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

The Gaiotto conjecture says that the category of representations of the quantum supergroup can be realized as a category of certain sheaves on the affine Grassmannian. It is the quantum version of a particular case of the relative Langlands conjecture by Ben-Zvi-Sakellaridis-Venkatesh. In this talk, we will mainly focus on the tamely ramified version of the Gaiotto conjecture, and see the application of the factorization method in its study. The talk is organized as follows, first we will review the background and explain the statement of the conjecture; then we will roughly sketch the strategy of the proof using the factorization method; if time permits, we will explain the application of the factorization method in the general relative Langlands program. The talk is based on ongoing works with Michael Finkelberg and Roman Travkin.

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Date/Time : 01 Sep 2025 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Wenqiang Xu, New York University

Are there infinitely many quadratic characters (for instance, the Legendre symbol mod p) for which the partial sums are always non-negative? This is a classical question that goes back to Fekete and Polya in 1911. Although only 0% of characters can have this property, numerical work (most recently by Kalmynin) suggests that such characters are nevertheless plentiful. For instance, computations show that there are many more examples than may be expected by modeling such sums by a simple random walk. I will discuss joint work with Angelo and Soundararajan which obtains new upper bounds for the number of such characters, by studying a related problem on maxima of L-values (closely connected to the Fyodorov–Hiary-Keating conjectures). I will give a heuristic explanation for why such characters are plentiful, which suggests that our upper bounds may not be too far from the truth.

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Date/Time : 19 Aug 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : York Ye, National University of Singapore

Configuration spaces of flags can be used to describe many algebraic varieties appearing in representation theory, such as double Bruhat cells and surface character varieties. In this talk, I will discuss the relationship between configuration spaces and cluster algebras. Then I will introduce my joint work with Huanchen Bao on the upper cluster structure of Kac-Moody Richardson varieties and explain some of the new techniques.

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Date/Time : 16 Jul 2025 15:00
Venue : S17 #04-04 (SR3)
Speaker : Naihuan Jing, North Carolina State University

I will discuss some polynomials parameterized by Young diagrams, whose coefficients are central elements of the quantized enveloping algebra of the general linear algebra. These polynomials are q-immanants and are shown to provide the higher quantum Capelli identities and generalize Drinfeld-Reshetikhin’s construction of central elements in Z(U_q(g)) as well as q-analogues of Okounkov’s quantum immanants for U(gl(n)). The Harish-Chandra image of the these central elements are certain factorial Schur polynomials. The main results are joint works with Ming Liu and Alex Molev.

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