Title: Arnold-Thom conjecture for the arrival time of surfacesAbstract: Following Łojasiewicz's uniqueness theorem and Thom's gradient conjecture, Arnold proposed a stronger version about the existence of limit tangents of gradient flow lines for analytic functions. In this talk, I will explain the proof of Łojasiewicz's theorem and Arnold's conjecture in the context of arrival time […]
Title: Near-center derivatives and arithmetic 1-cycles Abstract: Degrees of arithmetic special cycles on Shimura varieties are expected to appear in first derivatives of automorphic forms and L-functions, such as in the Gross--Zagier formula, Kudla's program, and the Arithmetic Gan--Gross--Prasad program. I will explain some “near-central” instances of an arithmetic Siegel--Weil formula from Kudla’s program, which […]
Title: Transfer operators in the language of quantization. Reference: https://arxiv.org/abs/2111.03004
Title: Some recent developments on the fully nonlinear Yamabe problems Abstract: In recent joint work with YanYan Li and Zongyuan Li, we broaden the scope of fully nonlinear Yamabe problems by establishing optimal Liouville-type theorems, local gradient estimates, and new existence and compactness results for conformal metrics on a closed Riemannian manifold with prescribed symmetric functions […]
Title: Stable Reduction via the Log Canonical Model.Abstract: We will discuss a natural perspective on stable reduction that extends Deligne--Mumford's stable reduction for curves to higher dimensions. From this perspective, we will outline a proof of stable reduction for surfaces in large characteristic.
Title: Beyond Endoscopy: Poisson Summation Formula and Kuznetsov Trace Formula on GL_2. Abstract: In the first part of the talk, we will give a direct proof of a Poisson summation formula on the Kuznetsov quotient of GL_2 that is responsible for the local Hankel transform calculated by H. Jacquet. In the second part of the […]
Title: The Sato–Tate ConjectureAbstract: We will motivate and state the Sato–Tate conjecture for elliptic curves. If we have time remaining, we will indicate how potential automorphy results are used in its proof.
Title: Covering Lemmas in Analysis and GeometryAbstract: Covering lemmas are fundamental tools in mathematical analysis, with deep connections to the geometry of Euclidean spaces. In this talk, we will explore key classical results, such as the Vitali and Besicovitch covering theorems, and discuss their significance in measure theory, differentiation, and geometric analysis.
Title: Asymptotics and Scattering for Relativistic Field Equations