ICTP Mathematics Seminar - Tuesday 17 September, at 14:30 - VENUE: Luigi Stasi Seminar Room - Shivang Jindal

[ICTP Math Section]

ICTP Mathemathics Seminar

Tuesday 17 Sep 2024, at 14:30

VENUE: ICTP Leonardo Building - Luigi Stasi Seminar Room


Title: Cohomological Hall algebra of curves and Quot schemes


Speaker: Shivang Jindal (University of Edinburgh)


Abstract: Given any smooth projective curve, one can define a Hall 
algebra-type structure on the cohomology of a moduli stack of coherent 
sheaves on the curve, called the cohomological Hall algebra of a curve 
(CoHA). In this talk, I will explain how CoHA is defined and show that 
CoHA naturally acts on the virtual homology of the Quot schemes. Virtual 
homology is a cohomological analog of the numerical invariants 
associated with the virtual fundamental class. If time permits, I will 
explain how one can define a double of the subalgebra of torsion sheaves 
and describe it in terms of generators and relations. This talk is based 
on joint work with Woonam Lim.