University of Leicester

Monday 3rd November 2008

- 11.00 am (F9, Maths Building): Coffee
- 12 noon, George Porter Lecture Room C:
Nicola Gambino (Dep. of Computer Science, Leicester)

"Homotopical Structures in Mathematical Logic" - 13.10 pm (eg Charles Wilson, 5th Floor): Lunch
- 2.30 pm, Physics Lecture room A:
James Cranch (Leicester/Sheffield)

"Span diagrams in homotopy theory" - 3.15 pm (F9 Maths Building): Tea
- 4.30 pm, Engineering Lecture Room 2:
Behrang Noohi (Kings College London)

"String topology for stacks"

Abstract: The aim of the talk is to give an overview of the recently-discovered connections between abstract homotopy theory and mathematical logic. These connections concern Quillen's homotopical algebra on the one hand and Martin-Loef set theory on the other hand. I will begin by giving an introduction to Martin-Loef set theory, assuming no prior knowledge of mathematical logic. Then, I will explain how the category of sets associated to Martin-Loef set theory admits a non-trivial weak factorisation system and relate this weak factorisation system to the natural Quillen model structure on the category of groupoids (joint work with Richard Garner). Finally, I will explain how these results fit into a general program, aimed at extending the correspondence between mathematical logic and category theory to higher-dimensional categories. Cranch: Span diagrams in homotopy theory

Abstract: This talk will report on my PhD thesis in preparation under Neil Strickland. I will supply some propaganda for the theory of quasicategories (due to Joyal and Lurie). Then I will show how Lawvere's notion of an algebraic theory carries across to this context. Lastly I will describe a new approach to homotopy commutativity equivalent to, and in some senses simpler than, the classical language of E_infinity operads. Noohi : String topology for stacks

Abstract: String topology (Chas-Sullivan, Cohen, Jones,...) studies the homology of the loop space of a manifold by exploiting the so-called string operations. With the goal of producing an equivariant version of the theory, we formulate string topology for topological stacks and prove the existence of string operations under certain natural hypotheses. As a consequence, we obtain equivariant string topology for compact Lie group actions on manifolds. This is a joint work with K. Behrend, G. Ginot, and P. Xu. (Reference: arXiv:0712.3857v1 [math.AT])

Tea and Coffee will be available in F9 Mathematics Building from 11am. There will be opportunity for those interested to find a drink/meal after the last talk; arrangements made on the day The TTT is partially supported by an LMS scheme 3 grant. Anyone who wishes to participate is welcome: we shall operate the usual arrangements for assistance with travel expenses . For further information email John Greenlees j.greenlees@sheffield.ac.uk, (or John Hunton jrh7@mcs.le.ac.uk or Nige Ray nige@ma.man.ac.uk) if you are interested, so we can make approximately the right amount of tea and coffee.

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