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Instanton counting on ALE spaces by means of framed sheaves

Le : 19/03/2013 14h15
Par : Francesco SALA (Heriot Watt University, Edinburgh)
Lieu : I 001
Lien web :
Résumé : In the present talk I will describe some relations between moduli spaces of framed sheaves on 2-dimensional toric orbifolds, basic representations of certain infinite-dimensional Lie algebras, and gauge theories on ALE spaces of type A_n. After a brief introduction about instantons and gauge theories on an ALE space X of type A_n, I will describe a conjectured relation between instantons on X and framed sheaves on a ``stacky compactification" of X. In the second part of the talk, I will focus on the case of framed sheaves on rank one: in this case the relation is proved and as an application we describe how this relation can be used to prove the Alday-Gaiotto-Tachikawa conjecture for (pure) U(1)-gauge theories.