Seminar
String Topology and Knots, Dr. Manuel Rivera, Purdue University, Mon, 3 November, 2025, 4:00 p.m. CNN A-142
Abstract
String topology studies algebraic structures arising from intersecting, concatenating, and splitting families of loops inside a manifold. The field began in the early 2000's with the foundational work of Chas and Sullivan, who discovered a Batalin-Vilkovisky (BV) algebra structure on the homology of the loop space of a manifold, an algebraic structure that also appears in the context of quantization in physics. Over the past decade, there has been a significant research activity 1) understanding the general structure of string topology, 2) clarifying its significance in mathematical physics and the geometry of manifolds, and 3) performing explicit computations of the structure. In this talk, I will give a broad overview of the subject, describe a relationship with the Skein algebra of knots discovered by Turaev, and outline several open questions and research directions. Post is here.