Elliptic cohomology and the Witten genus

Fall 2013

Stanford University

In this seminar we will (attempt to) understand the geometrical and physical underpinnings of the Witten genus.

DBE ran a similar seminar focusing on Kevin Costello's construction of the Witten genus using 2-d holomorphic Chern-Simons theory. Here are some notes from the talks.

Other helpful resources for the first few talks include Dan Freed's "Five Lectures on Supersymmetry," Witten's article "The Index of Dirac Operators," in Volume 1 of "Quantum Fields and Strings: A Course for Mathematicians," and Andy Neitzke's lecture notes on supersymmetric quantum mechanics.

All talks will be in 381-T, unless noted otherwise.

List of speakers and talks

Thursday October 3rd, 5pm, 383-N: Organizational meeting and some background, Daniel Berwick-Evans.

Wednesday October 23rd, 4:15pm: Dirac operators and supersymmetric quantum mechanics, Arnav Tripathy.

Wednesday October 30th, 4:15pm: The Dirac operator on loop space and the Witten genus, Arnav Tripathy.

Wednesday November 6th, 4:15pm: Construction of the Wiener measure on path space, Matthias Ludewig.

Wednesday November 13th, 4:15pm: Supersymmetric quantum mechanics and K-theory I, Daniel Berwick-Evans

Wednesday November 20th, 4:15pm: Supersymmetric quantum mechanics and K-theory II, Daniel Berwick-Evans

Wednesday December 4th, 4:15pm: Supersymmetric quantum mechanics and K-theory III, Daniel Berwick-Evans