BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jeremy Usatine (Brown University) DTSTART:20210430T131500Z DTEND:20210430T141500Z DTSTAMP:20260422T172521Z UID:TGiZ/22 DESCRIPTION:Title: St ringy invariants and toric Artin stacks\nby Jeremy Usatine (Brown Univ ersity) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstrac t\nStringy Hodge numbers are certain generalizations\, to the singular set ting\, of Hodge numbers. Unlike usual Hodge numbers\, stringy Hodge number s are not defined as dimensions of cohomology groups. Nonetheless\, an ope n conjecture of Batyrev's predicts that stringy Hodge numbers are nonnegat ive. In the special case of varieties with only quotient singularities\, Y asuda proved Batyrev's conjecture by showing that the stringy Hodge number s are given by orbifold cohomology. For more general singularities\, a sim ilar cohomological interpretation remains elusive. I will discuss a conjec tural framework\, proven in the toric case\, that relates stringy Hodge nu mbers to motivic integration for Artin stacks\, and I will explain how thi s framework applies to the search for a cohomological interpretation for s tringy Hodge numbers. This talk is based on joint work with Matthew Satria no.\n LOCATION:https://researchseminars.org/talk/TGiZ/22/ END:VEVENT END:VCALENDAR