PIRSA:15110090

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_15110090,
            doi = {},
            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}}
          }
          

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.)