Applying machine learning to algebraic topology: generating simplicial cycles

Abstract

We will discuss the philosophy of using generative models as sources of examples and counterexamples in contemporary algebra and homotopy theory. As an example of such application, we will look at the simplicial group setting of Wu’s formula, in which we reformulate a problem of generating simplicial cycles as a problem of sampling from the intersection of algorithmic datasets related to Dyck languages. A number of other possible directions and open problems will be dicussed. Based on the joint work with K. Brilliantov, D. Pasechnyuk, G. Magai.

Speaker Intro

I'm working in simplicial homotopy theory and its applications in path homology and homological algebra related to groups and Lie algebras. I'm also interested in applications of deep learning in contemporary mathematics.