Homotopical Methods in Geometry and Physics

Proceedings from a conference honoring Ezra Getzler reveal connections among geometry, topology, and mathematical physics. Featuring studies of moduli and configuration spaces, operad theory, and noncommutative geometry, the essays uncover how classical algebraic invariants are transformed through homotopical methods.

This volume contains the proceedings of the Homotopical Methods in Geometry and Physics Conference in honor of the 60th birthday of Ezra Getzler held at Northwestern University in Evanston, Illinois, on March 21-25, 2022. It includes papers on geometry and topology of moduli spaces and configuration spaces, on theory of operads, and on noncommutative geometry, as well as on various connections between these topics and on their role in mathematical physics. These topics have been extensively studied during the last forty years. One prominent feature of the subject is that various invariants of spaces, noncommutative algebras, etc. carry classical algebraic structures but only up to homotopy. Operations that are part of these structures form topological spaces (from polyhedra to configuration or moduli spaces) whose homotopy theory is of central importance. The same spaces can be viewed as configuration spaces in mathematical physics.