Séminaire Algèbre Géométrie Algébrique Topologie Algébrique :

Le 12 décembre 2019 à 11:30 - salle 430

Présentée par Minets Alexandre - IST Austria

K-theoretic Hall algebras of surfaces and quantum toroidal gl_n

The elliptic Hall algebra, also known as quantum toroidal gl_1, appears in a variety of geometric contexts, ranging from skein algebras to Hilbert schemes of points. I will explain how some of these appearances can be generalized to the quantum toroidal gl_n. Special attention will be paid to its relation with K-theoretic Hall algebras of surfaces. If time permits, I will try to sketch how this perspective may lead to a refinement of mirror symmetry for Hitchin systems of Donagi and Pantev.