K-theoretic Donaldson-Thomas theory and the Hilbert scheme of points on a surface

Integrals of characteristic classes of tautological sheaves on the Hilbert scheme of points on a surface often arise in enumerative problems. We explain how to use the K-theoretic Donaldson-Thomas theory of toric Calabi-Yau threefolds to study K-theoretic versions of such expressions.

Namely, we explicate a precise relationship between K-theoretic Donaldson-Thomas theory and the refined topological vertex of Iqbal, Kos├žaz and Vafa. Applying such results to specific toric threefolds, we deduce dualities satisfied by certain generating series that control integrals over the Hilbert scheme of points on a surface. We then explain how to use these dualities to evaluate certain Euler characteristics of tautological bundles on the Hilbert scheme of points on a general surface.

Collection/Series: 
Event Type: 
Seminar
Scientific Area(s): 
Speaker(s): 
Event Date: 
Monday, November 26, 2018 - 14:00 to 15:30
Location: 
Sky Room
Room #: 
394