All talks will be in the Michael Atiyah Building (MAB 119).
The morning coffee/tea will be served on the Ground Floor, Department of Mathematics, College House.
Here is a campus map: http://www2.le.ac.uk/maps/
Lunch may be taken in any of several local venues and we expect to visit a nearby restaurant for early evening dinner.
11.15 – 12.00

Tea, Coffee and Biscuits 
12.00 – 13.00

Matias del Hoyo (University of Utrecht) Integrating twoterm representations up to homotopy over Lie algebroids Lie
groupoids are a way to deal with singular smooth spaces. They
constitute a unified framework that includes manifolds, Lie groups,
actions, foliations and others. Lie algebroids are their infinitesimal
counterpart and together they play a rich theory in development. While
representations of groupoids and algebroids are too restrictive,
representations up to homotopy are flexible enough so as to contain
interesting examples.
Twoterm representations up to homotopy can be regarded as vector bundles over groupoids and algebroids, in the spirit of the socalled Grothendieck construction for lax functors. In this talk I will provide an overview of the topic and discuss the derivation and integration of vector bundles, part of a joint work with H. Bursztyn and A. Cabrera. 
13:00  14:30

LUNCH 
14:30 – 15:30

Ambrus Pal (Imperial College London) Simplicial homotopy theory of algebraic varieties over real closed fields I will talk about the homotopy type of the simplicial set of continuous definable simplexes of an algebraic variety defined over a real closed field, which I call the real homotopy type. There is an analogue of the theorem of Cox comparing the real homotopy type with the etale homotopy type, as well as an analogue of Sullivan’s conjecture which together imply a homotopy version of Grothendieck’s section conjecture. As an application I show that for geometrically rationally connected varieties over archimedean real closed fields the map from Requivalence classes to homotopy fixed points is a bijection, but it is not a bijection in general. Moreover there is a version of Grothendieck’s anabelian section conjecture for hyperbolic curves over real closed fields. 
16.00 – 17.00

Leila Schneps (Insitut de Mathematiques de Jussieu Paris) Braids, Galois groups and GrothendieckTeichmueller theory

Everyone who wishes to participate is welcome, particularly postgraduate students. We shall operate the usual criteria for assistance with travel expenses. Beneficiaries will need to complete the standard forms (available from the main TTT page), and should come with NI numbers and details of UK bank accounts if they want to complete the form on the day.