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
Title: Developing a library of formalized mathematics from a univalent point of view Abstract: The agda-unimath project started in November 2021, at a meeting called Univalent Foundations for Daily Applications. At this meeting, I proposed to formalize the Symmetry book project, in which group theory is studied from the perspective that symmetries are identifications in […]
Title: Finite time explosion for SPDEs Abstract: The classical existence and uniqueness theorems for SPDEs prove that, under appropriate assumptions, SPDEs with globally Lipschitz continuous forcing terms have unique global solutions. This talk outlines recent results about SPDEs exposed to superlinearly growing deterministic and stochastic forcing terms. I describe sufficient conditions that guarantee that, despite […]
Title: Cantor Dynamical Systems, Bratteli Diagrams, and Their Associated Full GroupsAbstract: If a countable group G acts on a Cantor set X, one can enlarge G to a (still countable) group F(G) by adding homeomorphisms of X that act locally as elements of G. This group, known as the full group of the dynamical system […]
Title: Du Bois invariants for isolated singularities.Abstract: The Du Bois invariants are natural invariants for singularities. In this talk, I will explain what they are, why they are interesting, and report on recent and ongoing work studying their properties.