This will be a working meeting. There will therefore be the usual time for
I will give an introduction to the basic techniques of parametrized homotopy theory and then apply them to derive well known classical results such as Poincar\'e duality and the Wirthm\"uller isomorphism.
The purpose of these two talks (the second is on Wednesday 7th) is to report on recent works which use stack theory to study derived categories. In the first talk I will discuss the problem of constructing a reasonable moduli space for compact objects in a given triangulated category (or rather a triangulated "dg-category"). In a first part I will explain some motivations coming from algebraic geometry and representation theory (e.g. the contruction of moduli spaces of complexes of sheaves on an algebraic variety, the definition of "Hall algebras" for derived categories). The second part of the talk will be devoted to present a solution to this problem using a notion of "derived \infty-stack": the main theorem states that the (derived \infty-) stack of compact objects in a given "saturated" dg-category is algebraic. Some corollaries and possible future applications will be discussed.
Anyone who wishes to participate is welcome: we shall operate the usual
arrangements for assistance with travel expenses. We expect to assemble for tea
and coffee in I15, Floor 5, from 11.00 am until the first talk. Each lecture
will take place in Room J11 of the Hicks Building, Hounsfield Road,
Tea and Coffee will be served in the common room I15.
For further information email John Greenlees firstname.lastname@example.org, (or John Hunton email@example.com or Nige Ray firstname.lastname@example.org) if you are interested, so we can make approximately the right amount of tea and coffee.