Algebra and geometry seminar 07-05-2021

[Francesco Galuppi]

Dear colleagues,

this is to advertise the weekly seminar of the Algebra and geometry 
group of University of Trieste. On Friday, May 7th at 9:30, Michail 
Savvas (University of California, San Diego) will talk about "Almost 
perfect obstruction theory and K-theoretic Donaldson-Thomas invariants".

Perfect obstruction theories are a fundamental ingredient used to define 
invariants associated to moduli problems, such as virtual cycles in the 
Chow group and virtual structure sheaves in K-theory. However, several 
moduli spaces, such as the moduli space of simple perfect complexes and 
desingularizations of moduli stacks of semistable sheaves on Calabi-Yau 
threefolds, do not admit a perfect obstruction theory. In this talk we 
introduce the relaxed notion of an almost perfect obstruction theory on 
a Deligne-Mumford stack and show that it gives rise to a virtual 
struture sheaf in K-theory. This applies to many examples of interest, 
including the above, and enables us to define K-theoretic invariants 
and, in particular, K-theoretic Donaldson-Thomas invariants of sheaves 
and complexes on Calabi-Yau threefolds. Based on joint work with 
Young-Hoon Kiem.

The seminar will take place online. The Zoom link is 
https://us02web.zoom.us/j/87239350702.

You are welcome to extend the invitation to anyone interested.