Lectures on Factorization Homology, ∞-Categories, and Topological Field Theories

Hiro Lee Tanaka is an Assistant Professor at Texas State University. Tanaka’s research with collaborators helped lay the foundations for the field of factorization homology. His current research involves applying infinity-categorical techniques to questions in symplectic geometry and mirror symmetryLukas Müller obtained his PhD in mathematical physics from Heriot-Watt University Edinburgh in 2020 and is a postdoctoral fellow at the Max-Planck-Institute for Mathematics in Bonn until 2022. His work lies mainly at the intersection of higher category theory, geometry and quantum field theory. He is also interested in quantum topology.Araminta Amabel is a PhD candidate at MIT, currently studying geometric topology through the lens of factorization homology.Artem Kalmykov is a PhD student at the Institute of Mathematics, University of Zurich. He obtained his bachelor’s degree at Higher School of Economics, Moscow, and Masterof Science at the University of Geneva. His research is mainly concerned with applications of the methods of derived algebraic geometry to representation theory, for instance, to the theory of quantum groups and elliptic algebras.

“These lecture notes provide an introduction to factorization homology … . These are very much lecture notes – the chapters were clearly written to accompany lectures. ... For me, the highlight of these notes are the numerous exercises of various levels of difficulty, designed to give the reader the tools to work in the field. These, together with a good technical discussion … make these notes a valuable tool for the serious reader seeking to learn factorization homology and related topics.” (Daniel Moskovich, zbMATH 1529.55001, 2024)“The reader with no prior knowledge of the subjects in the title of the book will … have an idea of topological field theory, an appreciation of the utility of ∞-categories, and the ability to articulate the definition of the new and exciting factorization homology theory. … A more experienced reader is likely to quite enjoy the ride that ties together various classical notions through one single Kan extension.” (Ittay Weiss, MAA Reviews, May 9, 2021)

• The one-dimensional case.- Factorization homology in higher dimensions.- Topological field theories and the cobordism hypothesis.