P^nfunctors and cyclic covers
Timothy Logvinenko (University of Cardiff)
What 


When 
May 03, 2018 from 03:30 pm to 04:30 pm 
Where  Mainz, 05432 (Hilbertraum) 
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Abstract.
I will begin by reviewing the geometry of a cyclic cover branched in a divisor. I will then explain how it gives the first ever example of a nonsplit P^nfunctor.
Given a sphere or a complex projective space on a Lagrangian manifold Y, one can construct a certain natural symplectomorphism of Y called a Dehn twist. Spherical and P^nfunctors are mirror symmetrical equivalents of this. These are functors between derived categories of algebraic varieties which induce natural autoequivalences known as spherical or P^ntwists. They arise naturally in many contexts related to moduli spaces or geometric representation theory.
If there is time, I will also explain the connection with the notion of a perverse schober introduced recently by Kapranov and Schechtmann.
This is a joint work with Rina Anno (Kansas).