Sixty-second meeting of the Transpennine Topology Triangle



The Open University, Sharston, Manchester
Tuesday
4/12/07


This will be a working meeting. There will therefore be the usual time for participant discussion.


Programme




We expect to go to eat nearby, soon after the last talk.

Abstracts

Talk: Richard Hepworth, "Orbifold Morse Theory."
Abstract: Morse theory is a geometric way to understand the homology of manifolds. Orbifolds are spaces that locally look like the quotient of a manifold by a finite group. Can we generalize Morse theory to orbifolds? I will explain how this question relates to the `crepant resolution conjecture' and give details of the answers I have obtained so far.

Talk: Martin Crossley, "Conjugation Invariants and Reed-Muller Codes."
Some years ago Sarah Whitehouse and I tried to compute the subalgebra of the dual Steenrod algebra consisting of those elements fixed by the Hopf algebra conjugation. Recently we have been using the free Hopf algebra generated by the Steenrod squares to shed light on this problem. While we haven't yet solved the conjugation invariants problem, our work has revealed an interesting link with Reed-Muller codes.

Talk: Frank Neumann, "Moduli stacks of vector bundles over algebraic curves and Frobenii"
Abstract: After giving an introduction into moduli problems and moduli stacks, I will describe the l-adic cohomology ring of the moduli stack of vector bundles on an algebraic curve in positive characteristic and will explicitly describe the action of the various geometric and arithmetic Frobenius morphisms on the cohomology ring. It turns out that using the language of algebraic stacks instead of geometric invariant theory this becomes surprisingly easy and topolgical in flavour. If time permits I will indicate how to prove the analogues of the Weil conjectures for the moduli stack. This is joint work in progress with Ulrich Stuhler (Goettingen).


Anyone who wishes to participate is welcome: we shall operate the usual arrangements for assistance with travel expenses.
Please email Gareth Williams G.R.Williams@Open.ac.uk if you are planning to attend. (or John Greenlees j.greenlees@sheffield.ac.uk, or John Hunton jrh7@mcs.le.ac.uk or Nige Ray nige@ma.man.ac.uk)


How to get there

Travel by rail to Manchester AIRPORT, then take a taxi to "The Open University, 351 Altrincham Road, Sharston, M22 4UN". Please obtain receipts for travel, and to minimise costs, please coordinate your taxi with other participants from your home institution. Manchester-based colleagues may prefer to take the 104 bus from (Higher) Cambridge Street to "Altrincham Road / The Open University" (services every 30 minutes). Taxis will be organized to take people back to the airport after the event.
The meeting is partially supported by a Scheme 3 grant from the London Mathematical Society.

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