Tuesday

4/12/07

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

- 11.00 am: Coffee

- 12 noon Richard Hepworth (Sheffield)

"Orbifold Morse Theory." - 2.30 pm, Martin Crossley (Swansea)

"Conjugation Invariants and Reed-Muller Codes." - 3.30 pm: Coffee
- 4.00 pm, Frank Neumann (Leicester)

"Moduli stacks of vector bundles over algebraic curves and Frobenii"

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

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)

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

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