University of Manchester

Thursday 29th January 2004

Titles and speakers are as follows.

- 11.00-11.30: TEA (Brian Hartley Room, Maths Tower, floor 6)

- 11.30-12.25 pm:

Matthias Franz (Geneva)

The cohomology of smooth toric varieties

- 12.30 pm: LUNCH

- 2.00-2.55 pm:

Dietrich Notbohm (Leicester)

On the homotopy type of Davis-Januszkiewicz spaces

- 3.00 pm: TEA (BHR)

- 3.30-4.25 pm:

Peter Symonds (UMIST)

Cohomology of profinite groups

Title: The cohomology of smooth toric varieties

Abstract: Smooth toric varieties are certain (not necessarily compact) complex manifolds with an action of a torus. They admit a combinatorial description in terms of convex-geometric data. We show how to recover the integral cohomology of a smooth toric variety from its equivariant cohomology. This is actually a special case of a more general result relating (equivariant) cohomology to Koszul duality.

Dietrich Notbohm (Leicester)

Title: On the homotopy type of Davis-Januszkiewicz spaces

Abstract: For an arbitrary simplicial complex $K$, Davis and Januszkiewicz have defined a family of homotopy equivalent CW-complexes whose integral cohomology rings are isomorphic to the Stanley-Reisner algebra of $K$. Subsequently, Buchstaber and Panov gave an alternative construction, which they showed to be homotopy equivalent to Davis and Januszkiewicz's examples. It is therefore natural to investigate the extent to which the homotopy type of a space $X$ is determined by having such a cohomology ring. We will discuss the associated rational and p-adic homotopy uiniquess question separately. Finally we can apply Sullivan's arithmetique square to produce global results in special families of cases.

Peter Symonds (UMIST)

Title: Cohomology of profinite groups

Abstract: We consider various properties of the cohomology of profinite groups. In the discrete case an important role is played by a contractible space of finite dimension on which the group acts with finite stabilizers. We develop an algebraic analogue for profinite groups.

Lunch will be taken locally (at the vegetarian "On the Eight Day", for example), and we expect to visit a local curry house (or similar) early in the evening.

Everyone who wishes to participate is welcome: we shall operate the usual arrangements for assistance with travel expenses. Please email Taras Panov tpanov@maths.man.ac.uk (or John Greenlees j.greenlees@sheffield.ac.uk, or John Hunton jrh7@mcs.le.ac.uk, or Nige Ray nige@maths.man.ac.uk) if you are interested in attending, so that we can cater for appropriate numbers.

The meeting is partially supported by a Scheme 3 grant from the London Mathematical Society.

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To TTT44