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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Date/Time : 26 May 2025 14:00
Venue : S17 #04-05 (SR2)
Speaker : Gus Lehrer, University of Sydney

I shall show how to use algebraic geometric methods to convert invariants of OSp into invariants of GL. This will be used to obtain precise versions of the first and second fundamental theorems for OSp.

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Date/Time : 16 Apr 2025 9:30
Venue : S17 #05-11 (SR5)
Speaker : Jishnu Kundu, National University of Singapore

The Relative Trace formula is a generalization of the Arthur Selberg trace formula and has its role in better understanding the automorphic representations of a general reductive group G. The talk will concern about the terms contributing to the spectral and geometric sides of the formula and concluded by a number theoretic application of it.

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Date/Time : 16 Apr 2025 10:20
Venue : S17 #05-11 (SR5)
Speaker : Leong Jin Ming, National University of Singapore

One of the main “conjectures” in the Relative Langlands Duality program launched by Ben-Zvi, Sakellaridis and Venkatesh is a duality between anomaly free hyperspherical pairs. In this talk we will explore the concept of anomaly freeness and use an equivalent representation theoretic formulation to work out which pairs are anomaly free.

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Date/Time : 15 Apr 2025 14:00
Venue : S17 #05-11 (SR5)
Speaker : Yotsanan Meemark, Chulalongkorn University

For a finite ring R with identity the unitary Cayley graph of R, C_R, is the graph with vertex set R and for each x, y in R, x and y are adjacent if and only if x-y is a unit of R. In this talk we will discuss many results on the structure parameters (e.g., clique number, chromatic number) and eigenvalues of this graph. We analyze the energy (the sum of eigenvalues) and characterize the ring R such that C_R is Ramanujan. Our combinatorial number-theoretic approaches mainly come from properties of finite rings and fields and their characters.

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Date/Time : 09 Apr 2025 10:00
Venue : S17 #05-11 (SR5)
Speaker : Edmund Karasiewicz, National University of Singapore

In this mini course we will study two topics. The first is the PGL2xF4 exceptional theta correspondence over a p-adic field. The second is the dual group of a spherical variety. Over the course of four lectures we will:

1. Introduce exceptional groups, focusing on constructions and tools relevant to the exceptional theta correspondence.
2. Describe the PGL2xF4 exceptional theta correspondence over a p-adic field.
3. Present the combinatorial construction of the dual group of a spherical variety due to Knop-Schalke.
4. Connect the exceptional theta correspondence to the F4/Spin9 spherical variety.

Join Zoom Meeting
https://nus-sg.zoom.us/j/84884850855?pwd=bvokLMShAf5wFeAHh2zemmel1dvb9f.1

Meeting ID: 848 8485 0855
Passcode: 226224

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