17:00
Canonical triangulations of quasifuchian convex cores
Abstract
Kleinian groups with an interesting deformation theory. I will show that the convex core of the quotient of hyperbolic 3-space by such a group admits a decomposition into ideal tetrahedra which is canonical in two completely independent senses: one combinatorial, the other geometric. One upshot is a proof of the Bending Lamination Conjecture for such groups.
14:15
Non Archimedian Geometry and Model Theory
Abstract
We shall present work in progress in collaboration with E. Hrushovski on the geometry of spaces of stably dominated types in connection with non archimedean geometry \`a la Berkovich
13:00
Elliptic curves, Cherednik Hecke algebras and Macdonald polynomials I
Abstract
We provide a realization of Cherednik's double affine Hecke
algebras (for GL_n) as a convolution algebra of functions on moduli spaces
of coherent sheaves on an elliptic curve. As an application we give a
geometric construction of Macdonald polynomials as (traces of) certain
natural perverse sheaves on these moduli spaces. We will discuss the
possible extensions to higher (or lower !) genus curves and the relation
to the Hitchin nilpotent variety. This is (partly) based on joint work
with I. Burban and E. Vasserot.
16:00
Motivic measure for pseudo-finite like fields
Abstract
To understand the definable sets of a theory, it is helpful to have some invariants, i.e. maps from the definable sets to somewhere else which are invariant under definable bijections. Denef and Loeser constructed a very strong such invariant for the theory of pseudo-finite fields (of characteristic zero): to each definable set, they associate a virtual motive. In this way one gets all the known cohomological invariants of varieties (like the Euler characteristic or the Hodge polynomial) for arbitrary definable sets.
I will first explain this, and then present a generalization to other fields, namely to perfect, pseudo-algebraically closed fields with pro-cyclic Galois group. To this end, we will construct maps between the set of definable sets of different such theories. (More precisely:
between the Grothendieck rings of these theories.) Moreover, I will show how, using these maps, one can extract additional information about definable sets of pseudo-finite fields (information which the map of Denef-Loeser loses).
14:45
16:30