# The AGT conjecture for gauge theories on A-type ALE spaces, K-theoretic/Cohomological Hall algebras and sheaves on stacks

### APA

Dimofte, T. (2015). The AGT conjecture for gauge theories on A-type ALE spaces, K-theoretic/Cohomological Hall algebras and sheaves on stacks. Perimeter Institute. https://pirsa.org/15110090

### MLA

Dimofte, Tudor. The AGT conjecture for gauge theories on A-type ALE spaces, K-theoretic/Cohomological Hall algebras and sheaves on stacks. Perimeter Institute, Nov. 12, 2015, https://pirsa.org/15110090

### BibTex

@misc{ pirsa_PIRSA:15110090, doi = {10.48660/15110090}, url = {https://pirsa.org/15110090}, author = {Dimofte, Tudor}, keywords = {Mathematical physics}, language = {en}, title = {The AGT conjecture for gauge theories on A-type ALE spaces, K-theoretic/Cohomological Hall algebras and sheaves on stacks}, publisher = {Perimeter Institute}, year = {2015}, month = {nov}, note = {PIRSA:15110090 see, \url{https://pirsa.org}} }

Tudor Dimofte University of Edinburgh

## Abstract

K-theoretical/Cohomological Hall algebras, associated with the stack of zero-dimensional sheaves on $\mathbb{C}^2$, play a prominent role in the proof, given by Schiffmann and Vasserot, of the AGT conjecture for

(pure) gauge theories on $\mathbb{C}^2$. In the present talk I will describe K-theoretic/Cohomological Hall algebras associated with stacks of torsion sheaves on A-type ALE spaces and their representations; the study of these algebras will provide eventually an approach to prove the AGT conjecture for (pure) gauge theories on A-type ALE spaces. (Work in progress with Olivier Schiffmann.)