Welcome to my home page!
My mentor is Rahul Pandharipande.
The focus of my research is motivic homotopy theory,
which applies powerful methods of algebraic topology
to shed light on mysteries of algebraic geometry.
"The more I learned, the more conscious did I become of the fact that I was ridiculous. So that for me my years of hard work at the university seem in the end to have existed for the sole purpose of demonstrating and proving to me, the more deeply engrossed I became in my studies, that I was an utterly absurd person."
Fyodor Dostoevsky, The Dream of a Ridiculous Man
Title: What is... an infinity-category?
Abstract: In different areas of mathematics it is convenient to work with categories, i.e., with sets of objects (possibly united by some property) and morphisms between them. However, when it comes to objects of topological nature, we often would like to consider the higher structure of morphisms between morphisms. For examples, higher structures are relevant when we work with topological spaces, continuous maps and homotopies, or with smooth manifolds, their cobordisms and diffeomorphisms between them. A generalization of a category that allows to encode the data of (infinitely many) higher morphisms is the notion of an infinity-category. In this talk, I will give a definition of an infinity-category and explain some of the main ideas behind this concept, as well as provide various examples.