Alan Turing Building

University of Manchester

Monday Monday 19 January 2009

The talks will take place in the Frank Adams Seminar Rooms 1 and 2, on the first floor of the Alan Turing Building. This is on the east side of the campus, off Upper Brook Street and about 100m south of the junction with Booth Street East. It is about 15 minutes walk from Piccadilly station, through the old UMIST campus and under the Mancunian Way. The building is number 46 on the University Campus map.

Participants will meet for coffee from 1100AM onwards in the Atrium Bridge Common Room; the Frank Adams Rooms open into the common room.

Lunch may be taken in any of several local venues (such as the cafe in the atrium, or the vegetarian "On the Eighth Day", for example), and we expect to visit a nearby restaurant for early-evening dinner.

- 11.00-11.30: COFFEE (Atrium Bridge)

- 11.30-12.30: Tony Bahri (Rider University, NJ USA)

**Piecewise Polynomials and the Equivariant Cohomology of Toric Varieties**

*Toric varieties have a natural torus action. For smooth varieties, the integral equivariant cohomology with respect to this action is the Stanley-Reisner ring of the underlying fan. A description of this ring in terms of piecewise polynomials on the fan allows a generalization to a class of singular varieties which include weighted projective spaces. Unlike ordinary cohomology, the integral equivariant cohomology distinguishes among weighted projective spaces.*[A report on joint work with Matthias Franz and Nigel Ray] - 12.30-2.30: LUNCH

- 2.30-3.30: Al Kasprzyk (Kent)

**Simplices in toric geometry: Fake weighted projective space**

*When considering toric Fano varieties, it is natural to think about simplices. In this talk I'll concentrate on one-point lattice simplicies and their associated varieties: fake weighted projective space. I hope to illustrate the difference between fake and genuine weighted projective space, and give several example calculations.* - 4.00-5.00: Jon Woolf (Liverpool)

**What are the homotopy groups of a stratified space?**

*The usual definition of homotopy groups makes perfect sense when the space is stratified, but are there subtler invariants which capture some of the extra information in the stratification? This talk will introduce two proposals (due respectively to MacPherson and Baez) for modifying the definition of the homotopy groups of a stratified space, illustrated by some simple examples. For MacPherson's proposal I will discuss the analogue(s) of the fact that the fundamental group classifies covering spaces and for Baez's I will discuss a conjectural relation to bordism theory.*

Everyone who wishes to participate is welcome, particularly postgraduate students. We shall operate the usual criterea for assistance with travel expenses, but beneficiaries will need to complete the standard forms, and should come armed with NI numbers and details of UK bank accounts. Please email nigel.ray(at)manchester.ac.uk if you expect to attend, so that we can cater for appropriate numbers.

The meeting is jointly supported by the London Mathematical Society and MIMS.

MIMS

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