Timothy Logvinenko
(Cardiff University)

Geometry and Topology Seminar

Monday, 4 November, 2019, at 15:15-16:15, in Koll. D (1531-211)

Description:

I will give a final overview of the theory of P^n-functors developed by Rina Anno and I in arXiv:1905.05740. After some formal definitions, I will concentrate on four new families of examples of non–split P^n-functors: spherical functors, extensions by zero, cyclic covers, and family P-twists. For the latter, I will explain the associated Mukai flop picture and the "flop-flop = twist" formula. I will then discuss our proof of Segal's conjecture: any split P^n-functor deforms to a spherical functor from a non-commutative line bundle over the base category. I will finish with some speculation: an approach to the converse of Segal's conjecture, the related question of whether the P^n-functor data can be 'reconstructed' from its first order truncation (the P-twist data), the reasons why Segal's conjecture doesn't generalise straightforwardly to non-split P^n-functors, and the relation between all this and a work in progress with Alexei Bondal on perverse schobers on orbifolds

Organised by: QGM

Contact person: Sergey Arkhipov