Eighty Second Meeting of the Transpennine Topology Triangle

University of Leicester
Friday 2nd December 2011 

Supported by the London Mathematical Society  


10:30 - 10:55

Foyer First Floor Engineering Building

Coffee, Tea and Biscuits

10:55 - 11:55 

Engineering Lecture Theatre 1 (ENG LT1)

Mark Grant (Nottingham)
Realizing homology classes by immersions

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

12:00 - 13:00

Engineering Lecture Theatre 1 (ENG LT1)

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 characterization of homotopical cocompleteness based on the existence of `homotopy coequalizers', interpreted as good homotopy colimits for diagrams of simplicial shape. This characterization might be understood as a homotopical version of the classical result stating that all colimits can be computed using coproducts and coequalizers.




14:30 - 15:30

George Porter Lecture Theatre B (GP LTB)

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 a recent work with G. Tomassini we have generalized 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.

15:30 - 16:00

Foyer Ground Floor George Porter Building

Coffee, Tea and Biscuits

16:00 - 17:00

George Porter Lecture Theatre B (GP LTB)

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.

Here is a link to a 3D campus map: http://www2.le.ac.uk/maps/campus-map

There will be a dinner after the talks (probably in a South Indian restaurant close to the station).

Everyone who wishes to participate is welcome, particularly postgraduate students. We shall operate the usual criteria for assistance with travel expenses, but beneficiaries will need to complete the standard forms (available from the main TTT page), and should come armed with NI numbers and details of UK bank accounts if they want to complete the form on the day. 

Escape routes

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