Date/Time : 02 Jan 2026 10:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Wei Zhang, MIT

In their 1986 paper, Gross and Zagier proved a formula relating the height of Heegner point on an elliptic curve to the first derivatives of the L-function of that elliptic curve. Since then, the problem of generalizing this fundamental result to higher dimensional algebraic varieties has been of great interest. In this talk we will present some of the generalizations with relatively recent results, with an emphasis on Kudla’s program and the arithmetic Gan-Gross-Prasad conjecture.

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Date/Time : 22 Dec 2025 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Xinwen Zhu, Stanford University

Let Sh_G be a Hodge type Shimura variety and let p be a prime such that G_{Q_p} is umramified. I will discuss the torsion vanishing type results for the Whitaker coefficients of depth zero part of cohomology of Sh_G as G(Q_p) representations. This is a joint work in progress with Ian Gleason and Xiangqian Yang. Title: Torsion vanishing of local Whittaker coefficients of cohomology of Shimura varieties. Abstract: Let Sh_G be a Hodge type Shimura variety and let p be a prime such that G_{Q_p} is umramified. I will discuss the torsion vanishing type results for the Whitaker coefficients of depth zero part of cohomology of Sh_G as G(Q_p) representations. This is a joint work in progress with Ian Gleason and Xiangqian Yang.

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Date/Time : 12 Dec 2025 15:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Yun GAO, Shanghai University

The Galilean conformal algebra is an infinite-dimensional extension of the finite-dimensional Galilean conformal algebra in (d+1) dimensional space-time. We use simple modules over the finite-dimensional solvable Lie algebras to construct many simple restricted modules.

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Date/Time : 25 Nov 2025 10:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Lo Chi-Heng , National University of Singapore

In this talk, I will discuss Jiang’s Conjecture, which predicts an upper bound for the wavefront set of any representation of Arthur type in terms of the local Arthur packet containing it. I will then describe its generalization to ABV-packets and to arbitrary irreducible representations (not necessarily of Arthur type), and show that all these formulations of Jiang’s Conjecture are in fact equivalent. Moreover, I will explain that these conjectures can be further reduced to the case of anti-tempered representations.

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Date/Time : 20 Nov 2025 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Yang Daodao, Eastern Institute of Technology, Ningbo

The metric theory of Diophantine approximation investigates whether typical real numbers can be well approximated by rational numbers. In 1924, Khintchine proposed the first 0-1 law in metric Diophantine approximation: assuming that the approximation function has a certain monotonicity, this law provides a necessary and sufficient condition for typical real numbers to be well approximated by infinitely many rational numbers. In 1941, Duffin and Schaeffer attempted to generalize Khintchine’s theorem without assuming that the approximation function has monotonicity. Their proposed new 0-1 law, known as the Duffin–Schaeffer conjecture, became a central problem in Diophantine approximation. After considerable efforts by many number theorists, the Duffin–Schaeffer conjecture was finally resolved by Koukoulopoulos and Maynard in 2019. A remaining challenge is to establish a quantitative law, similar to the strengthening of Khintchine’s theorem by Erdős and Schmidt, to estimate the number of reduced fractions that can approximate the given real number sufficiently well. In 2022, Aistleitner, Borda and Hauke established a quantitative version of the Duffin–Schaeffer conjecture, but the error term they obtained only achieved a logarithmic power-saving. An open problem is to establish an asymptotic formula with a power-saving error term. In a recent joint work with Koukoulopoulos and Maynard, we prove a quantitative version of the Duffin–Schaeffer conjecture with an almost sharp error term.

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Date/Time : 17 Nov 2025 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : He Xuhua, University of Hong Kong

Lusztig’s theory of canonical bases reveals a remarkably rigid and positive algebraic structure on quantum groups and their modules. A fundamental result in symmetric types establishes that the structure constants for multiplication in the negative part $U^-$, as well as for the action of Chevalley generators $E_i$ and $F_i$ on a single simple module, all belong to $\mathbb{N}[v, v^{-1}]$.

Lusztig conjectured that this strong positivity holds for the multiplication within the modified quantum group and the action on the tensor product of modules. In this talk, I will present recent joint work with my postdoc, Jiepeng Fang. Our main result establishes that the structure constants for both the multiplication with arbitrary canonical basis elements in $\dot{\mathbf{U}}$ and the action on the canonical basis elements of arbitrary tensor products of simple lowest and highest weight modules by canonical basis elements arising from spherical parabolic subalgebras belong to $\mathbb{N}[v,v^{-1}]$.

A key innovation in our proof is the “thickening philosophy”, an algebraic technique inspired by geometric ideas from total positivity, building on my earlier work with Huanchen Bao. This method embeds a suitable approximation of the tensor product into the negative part $\tilde{U}^-$ of a larger quantum group, constructed via a framed
quiver. This allows us to inherit the desired positivity directly from the well-established positivity of the canonical basis of $\tilde{U}^-$. This approach demonstrates how wild Kac-Moody groups can provide a powerful framework for elucidating the representation theory of quantum groups beyond finite and affine types.

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Date/Time : 17 Nov 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Wang Weiqiang, University of Virginia

As a degeneration of affine quantum groups, Yangians quantize current algebras. It is known that truncated shifted Yangians quantize affine Grassmannian slices of type ADE; the latter are Coulomb branches of framed quiver gauge theories, and in type A, they can be identified with nilpotent Slodowy slices. As a degeneration of affine iquantum groups, twisted Yangians quantize twisted current algebras. We explain the Poisson geometry of [truncated shifted] twisted Yangians in terms of fixed point loci of affine Grassmannian slices by Poisson involutions; in split type A, the latter are identified will nipotent Slodowy slices of type BCD. This is joint work with Kang Lu and Alex Weekes.

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Date/Time : 28 Oct 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Wang Weiqiang, University of Virginia/NUS

iQuantum groups arising from quantum symmetric pairs can be viewed as a generalization of Drinfeld-Jimbo quantum groups. Lusztig’s braid group symmetries for quantum groups and their modules have played an important role in understanding structures of quantum groups and applications. In this talk, we will present a construction of relative braid group symmetries for iquantum groups and modules by providing explicit rank one formulas and connection to Lusztig’s construction. This is joint work with Weinan Zhang (Hong Kong).

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Date/Time : 14 Oct 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Lo Chi-Heng, National University of Singapore

In this talk, I will first introduce the closure ordering conjecture for local Arthur packets. Then I will present a proof using the combinatorial structure of Ψ(π) that we studied last week.  I will also discuss two important consequences:

(1) a framework for proving the enhanced Shahidi conjecture for general groups, and
(2) a proof of Vogan’s conjecture on the coincidence of A-packets and ABV-packets of Arthur type for classical groups, under certain assumptions.

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