## Video URL

http://pirsa.org/23040101# Chern-Simons, time-reversal, bordism, and Smith homomorphisms.

### APA

Yu, M. (2023). Chern-Simons, time-reversal, bordism, and Smith homomorphisms.. Perimeter Institute for Theoretical Physics. http://pirsa.org/23040101

### MLA

Yu, Matthew. Chern-Simons, time-reversal, bordism, and Smith homomorphisms.. Perimeter Institute for Theoretical Physics, Apr. 14, 2023, http://pirsa.org/23040101

### BibTex

@misc{ scivideos_PIRSA:23040101, doi = {}, url = {http://pirsa.org/23040101}, author = {Yu, Matthew}, keywords = {Quantum Fields and Strings}, language = {en}, title = {Chern-Simons, time-reversal, bordism, and Smith homomorphisms.}, publisher = {Perimeter Institute for Theoretical Physics}, year = {2023}, month = {apr}, note = {PIRSA:23040101 see, \url{https://scivideos.org/index.php/PIRSA/23040101}} }

Matthew Yu University of Oxford

## Abstract

Chern-Simons theories can possess 't Hooft anomalies for time-reversal symmetry. In this talk, we will discuss abelian Chern-Simons theories with an interesting time-reversal symmetry algebra and compute the classification of the anomaly, which is captured by a bordism group. In order to get the classification correct I will explain the argument we used that utilized the Smith homomorphism for bordism groups. In order to compute the value of the anomaly we study the Atiyah-Hirzebruch spectral sequence and find a way to trivialize each layer of the anomaly. I will also discuss the generating manifold for the corresponding bordism group, and how it arises from the Smith homomorphism. The knowledge of this manifold allows one to compute the partition function by using the data that characterizes the Chern-Simons theory and the symmetry actions; this gives a robust check of our answer for the anomaly. This is based on work in progress with Arun Debray and Weicheng Ye.

Zoom link: TBA