A Brief Introduction to Gödel's Incompleteness Theorems In 1931 Kurt Gödel proved a pair of landmark results that limited the strength of formal theories of mathematics. These "incompleteness theorems" are […]
Title: Soap films, Plateau's laws, and the Allen-Cahn equation Abstract: Plateau's problem of minimizing area among surfaces with a common boundary is the basic model for soap films and leads to […]
Title: Finite approximations as a tool for studying triangulated categories.Abstract: A metric on a category assigns lengths to morphisms, with the triangle inequality holding. This notion goes back to a 1974 article […]
Title: On an application of the residue method. Abstract: When a period integral of an automorphic form converges and is not zero it is often related to a special value […]
Title: Kähler-Einstein metric, K-stability and moduli of Fano varieties I. Abstract: A complex variety with a positive first Chern class is called a Fano variety. The question of whether a […]
Title and abstract TBA
Title: Kähler-Einstein metric, K-stability and moduli of Fano varieties II. Abstract: Algebraic varieties are given by solutions of a system of polynomial equations. Constructing parameter space for them has roots […]
Title: First eigenvalue estimates on asymptotically hyperbolic manifolds and their submanifolds. Abstract: I will report on joint work with Samuel Pérez-Ayala. We derive a sharp upper bound for the first […]
Title: Six functor formalism and the !-topology
Title: The simply typed 2λ-calculus Abstract: 2λ-calculus is a language with three levels: types, terms, and rewrites. I will explore their properties and give categorical description of the equational theory […]