Wassilij Gnedin - Universität Paderborn   
Silting bijections and ribbon graph orders

In the nineties, Rickard studied tilting theory under change of rings. His results provide a bijection between tilting complexes of the algebra RG of a finite group G with coefficients in a complete local ring R and those of its finite-dimensional quotient kG over the residue field k of R. Further properties of this bijection yield an approach to study the derived Morita theory of one of the algebras in terms of the other.
My talk is concerned with a class of derived-tame algebras, called ribbon graph orders, which may be viewed as infinite-dimensional versions of gentle algebras as well as lifts of Brauer graph algebras. The latter include blocks of certain finite groups and have mostly derived-wild representation type.
The main goal of my talk is to establish a tilting bijection for any ribbon graph order and each of its Brauer graph algebra quotients. The way towards this goal leads naturally to extend Rickard's techniques in several directions: the study of silting complexes over Noetherian R-algebras and their behaviour modulo certain, not necessarily central elements.
In the last part of the talk, the tilting bijection will be applied to transfer the derived equivalence classification of Brauer graph algebras by Opper and Zvonareva to a similar solution for ribbon graph orders.