Tutorial Speakers
Titles and Abstracts
Evelyne Hubert
INRIA Méditerranée, France 
Preserving and Exploiting Symmetry in Algebraic ComputationAbstract:
I wish to first present a general approach to preserving and exploiting symmetry in algebraic computations that boil down to linear algebra in finite dimensional vector spaces of polynomials. This will be illustrated on the easily understood problem of multivariate interpolation, though the underlying principle applies to global optimisation, computing cubatures, as well as computations in physics and chemistry....
The key observation is that the matrices involved become block diagonal, with repeated blocks, in a symmetry adapted bases.

Pierre Lairez
INRIA Saclay and École polytechnique, France 
Transcendental methods in numerical algebraic geometryAbstract:
Numerical algebraic geometry is the art of using numerical approximations to study complex algebraic varieties through their points, where algebraic methods instead consider the equations and the rings they define. Transcendental methods emerge from the integration of algebraic functions; they express in a simple way certain very fine properties of varieties at the cost of introducing transcendent functions. The objective of this tutorial is to show how numerical algebraic geometry can exploit transcendental methods through high precision computation of algebraic integrals. 