TTT82: Leicester

University of Leicester.

Supported by the London Mathematical Society.  

Date

2 December 2011

Speakers

Mark Grant (Nottingham)
Realising homology classes by immersions

In every codimension greater than or equal to two there exists a mod 2 homology class in a closed smooth manifold which cannot be realised by an immersion. This is joint work with András Szucs (Eotvos Lorand).

Beatriz Gonzalez Rodriguez (ICMAT-CSIC Madrid)
Homotopical cocompleteness for relative categories closed by coproducts

In this talk we study homotopy colimits defined as left adjoints to the constant diagram functor in a suitable 2-category of relative categories. In case the relative category considered is closed by coproducts, we give a characterisation of homotopical cocompleteness based on the existence of 'homotopy coequalisers', interpreted as good homotopy colimits for diagrams of simplicial shape.

This characterisation might be understood as a homotopical version of the classical result stating that all colimits can be computed using coproducts and coequalisers.

Simone Borghesi (Milano-Bicocca)
Brody's theorem for Deligne-Mumford stacks

The classical Brody's theorem in complex geometry relates two notions of hyperbolicity of a complex space: it states that they are equivalent if the space is compact. In recent work with G Tomassini we generalised this theorem to Deligne-Mumford analytic stacks.

In this talk we will discuss the definitions of Kobayashi and Brody hyperbolicity for stacks, using an exotic homotopy theory, then I will mention about the key points in the proof of the theorem involving the use of complex variables in a framework dictated by the underlying homotopy theory.

Burt Totaro (Cambridge)
New bounds for the cohomology of finite groups

Symonds showed that the cohomology ring of a finite group G with a faithful complex representation of dimension n is generated by elements of degree at most n^2. This was a remarkable advance, since no bound was known before.

Symonds's proof combined equivariant cohomology with commutative algebra (Castelnuovo-Mumford regularity). We give better bounds for the cohomology ring of a p-group. For some problems of this type, we give optimal bounds.