Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

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.