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.

Add to calendar :

Date/Time : 24 Dec 2025 10:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Yi Zhou, Fudan University

We propose a new physical space approach to bilinear estimates for dispersive equations. We can use this method to give alternative proofs other than the Bourgain space method of low regularity well posedness for dispersive equations. We can also use this method to give alternative proofs of global existence with small initial data for nonlinear wave equations. Moreover, we get new results including the global existence for one dimensional periodic Schrodinger map flow and global well psodness in the critical Besov space of Skew mean curvature flow in high dimensions.

Add to calendar :

Date/Time : 24 Dec 2025 11:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Hong Kiat Tan, University of California, Los Angeles

2 x 2 systems of hyperbolic conservation laws arise throughout the physical sciences, such as in isentropic gas dynamics (the p-system), vehicular traffic flow models, shallow water equations, and particle-laden flows equations. A fundamental question for such systems concerns the structural stability of Riemann solutions, that is, whether the qualitative structure of shock and rarefaction waves persists under perturbations of the flux function and initial data.

In this talk, I will present a proof of generic structural stability for Riemann solutions to 2 × 2 systems of hyperbolic conservation laws in one spatial dimension. Specifically, we show that for almost every left and right states, shocks and rarefaction solutions of the same wave type are preserved under perturbations of the flux functions and the initial data. The proof requires the standard assumptions of strict hyperbolicity and genuine nonlinearity, together with geometric conditions motivated by differential topology, such as the regular manifold assumption.

The proof proceeds in two stages. First, we establish that transversality of the wave curves (the Hugoniot loci and rarefaction curves) implies structural stability of the Riemann solution. Next, we invoke a variant of Thom’s parametric transversality theorem to show that this transversality condition holds generically in the left and right states. We conclude by discussing applications of the theorem to numerical analysis and approximation schemes for 2 × 2 systems of conservation laws.

Add to calendar :

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.

Add to calendar :

Date/Time : 16 Dec 2025 14:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Yongchun Li, The Chinese University of Hong Kong

The low-rank constrained optimization arises in various machine learning and operations research problems. It minimizes a linear objective function subject to multiple two-sided linear inequalities and a low-rank domain set. Although the low-rank constrained optimization is generally NP-hard, a viable approach is to convexify the domain set (i.e., replace the domain set with its convex hull), known as “partial convexification.” Partial convexification often leads to a tractable convex relaxation; however, its solution quality lacks theoretical guarantees. To fill this gap, (i) we establish the necessary and sufficient condition under which the partial convexification matches the original low-rank constrained optimization; and (ii) we derive an upper bound on the minimum rank among all the optimal solutions of the partial convexification and prove its tightness. To efficiently solve the partial convexification, we develop a column generation algorithm combined with a rank-reduction algorithm. This combination ensures that the output solution satisfies the theoretical guarantees. Finally, our numerical experiments validate the strength of the partial convexification and the effectiveness of the proposed algorithms.

Add to calendar :

Date/Time : 15 Dec 2025 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Yuta Takaya, Tokyo University

In the local Langlands program, both local Shimura varieties and type theory play important roles. Although the relationship between these two approaches remains largely open, starting from the work of Yoshida and Boyarchenko-Weinstein, it has been observed that certain affinoids around CM points in Lubin-Tate spaces reflect the associated type theory. In this talk, I will introduce analogous affinoids around unramified CM points in general local Shimura varieties, and explain the relation to regular depth-zero supercuspidal representations. If time permits, I will provide an outlook on the extension to positive depth.

Add to calendar :

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.

Add to calendar :

Date/Time : 12 Dec 2025 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Su Chunmei, Tsinghua University

The quality of the mesh is crucial for simulating curvature flows, as standard approaches may fail due to mesh distortion. We first present a series of high-order parametric finite element methods based on the BGN formulation for solving various types of flows involving curves and surfaces. Extensive numerical experiments demonstrate the anticipated high-order accuracy while maintaining favorable mesh quality throughout the evolution process. Secondly, for flows involving multiple geometric structures, such as surface diffusion—which reduces area while preserving volume—we propose a type of structure-preserving method that incorporates two scalar Lagrange multipliers along with two evolution equations related to area and volume, respectively. These schemes effectively preserve the geometric structure at a fully discrete level. Comprehensive numerical experiments illustrate that our methods achieve the desired temporal accuracy, while simultaneously preserving the geometric structure of the surface diffusion.

Add to calendar :

Date/Time : 11 Dec 2025 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Ivan Fesenko, Westlake University, China

Zeta functions are the central object in number theory.

Iwasawa and Tate independently described how using adelic structures from class field theory one can obtain an integral presentation for zeta functions of number fields and prove their key properties (except the generalised Riemann hypothesis). They used Haar measure on abelian locally compact groups and associated harmonic analysis.

Modern number theory often works with two-dimensional objects such as elliptic curves over number fields and their proper regular models. Associated 2d local and adelic structures are far from locally compact. It was an open problem to produce a 2d version of the Iwasawa-Tate theory. The speaker introduced higher Haar measure and integration on 2d local and adelic objects and used them to establish such a 2d generalisation. This talk will briefly present this 2d theory and how it further leads to a new approach to the Birch and Swinnerton-Dyer conjecture.

Add to calendar :