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.
Title: A survey of enriched categoriesAbstract: We'll recall some rudiments of the notion of a category, including some examples such as the category Set of sets and functions, the category Vect of vector spaces and linear maps, the category Top of topological spaces and continuous maps, etc. We'll then delve into the notion of an enriched category, where […]
Title: Affine and asymptotic Hecke algebras Abstract: Affine Hecke algebras play a prominent role the representation theory of p-adic groups, where a large subcategory of representations are equivalent to modules over the affine Hecke algebra. The important subcategory of tempered representations is equivalent to modules over a larger ring, the Harish-Chandra Schwartz algebra. However, this […]
Title : Scalar curvature comparison and rigidity of 3-dimensional weakly convex domains Abstract: I will discuss a comparison and rigidity result of scalar curvature and scaled mean curvature on the boundary for weakly convex domain in Euclidean space, which is a joint work with Xuan Yao. This result is a smooth analog of Gromov's dihedral […]
Title: "On applications of Topology" Abstract: I will explain how knowledge of Topology helped with winning the Nobel Prize in Physics 2016. No familiarity with advanced math beyond Calculus will be assumed from the audience.