Lectures on topological phases for mathematicians (2018/2019/2020)

Overview

Here I collect the notes of my lectures on topological phases for mathematicians. Notes have a lot of overlaps.

[Notes] Jan 26-28, 2020 at Komaba

I will explain that the classification of invertible phases is given by the Anderson and/or Pontryagin dual to the bordism group.

[Notes] Feb 12-15, 2019 at Komaba

After reviewing the Atiyah-Segal-like approach to QFTs, I discussed finite group gauge theories and their anomalies.

[Notes] Dec 20, 2017 at IPMU & May 24, 2018 at Riken

I discussed why invertible/SPT phases are classified by generalized cohomology theories. The notes are very sketchy. The original version used at IPMU was written in blue-black, and the additions in red were for the talk in Riken.

email: yuji.tachikawa_at_****.**