Speaker: Andreas Hochenegger 
Università di Milano

Title:
Formality of P-objects.

Abstract:
An Calabi-Yau-object in a k-linear triangulated category is called a 
P-object, if its derived endomorphism ring is isomorphic to k[t]/t^n. 
They were first studied by Daniel Huybrechts and Richard Thomas as 
generalisations of spherical objects. Similar to the spherical case, 
P-objects induce autoequivalences which are called P-twists.
Recently, Ed Segal showed how an arbitrary autoequivalence can be 
written as a spherical functor. For a P-twist, he needs the assumption 
that the endomorphism ring of the P-object is formal.
In this talk, I will introduce the concept of formality and present a 
proof of the formality of P-objects. This is based on a joint work in 
progress with Andreas Krug.