Pierre Godfard

The Witten-Reshetikhin-Turaev SO(3) modular functors are families of 
finite-dimensional representations of Mapping Class Groups of surfaces, 
with strong compatibility conditions. Each choice of odd integer r and 
primitive r-th root of unity yields such a modular functor.
Mapping Class Groups of surfaces are isomorphic to fundamental groups of 
moduli spaces of curves. Hence modular functors can be alternatively 
seen as families of flat vector bundles on moduli spaces of curves.

These flat vector bundles are expected to be rigid (in genus g>=3) and 
thus support complex variations of Hodge structures.

In this talk, we will discuss a geometric construction of the SO(3) 
modular functors in genus 0 based on homological models of 
Felder-Wieczerkowski and Martel. We will explain how this construction 
proves the existence of integral variations of Hodge structures on the 
SO(3) modular functors in genus 0 and how one can compute their Hodge 
numbers.