July 6 -10, 2015
Within the last fifteen years, Dynamics and geometry in the Teichmüller space is and area that has known considerable progress and to which many first-class mathematicians have contributed. One such recent development is a theorem by Eskin and Mirzakhani that proves that complex geodesics and their closures in moduli space are surprisingly regular, rather than irregular or fractal, a fantastic new path that revolutionizes this area of research and was announced in 2012.
The main topics we want to focus on in this workshop are at the border with geometry, algebraic geometry, topology, dynamical systems, ergodic theory and number theory.
We are aiming at four fifty-minute talks per day and a total of 18 talks. This format is particularly adapted as it leaves a lot of space for discussion and informal work in smaller groups. This conference is aimed at experts in those areas but is also particularly designed for young researchers.
Artur Avila (Université Paris Diderot)
Pascal Hubert (Aix-Marseille Université)
Classification of Higher Rank Orbit Closures in Hyperelliptic Components of Strata and Finiteness Results for Teichmuller Curves
On « Circle » Averages on Flat Surfaces
The Hurwitz Constant is Isolated in Each Stratum
Stability of Minimal Interval Exchange Transformations
On the Algebraic Hull of the Kontsevich-Zorich Cocycle and Applications to Finiteness Theorems
Zero Lyapunov Exponents of the Kontsevich-Zorich Cocycle
On the Ergodicity of Billiards in Non-Rational Polygons
Limits of (Real-Normalized) Meromorphic Differentials and their Zeroes on Nodal Riemann Surfaces
Generic Measures for Interval Exchange Transformations
Coupled Rotations and Snow Falling on Cedars
On Renormalized Volume
Quasimodularity of Siegel-Veech Constants and Large Genus
Kronecker’s Congruence and Teichmuller Curves in Positive Characteristic
Cohomology Classes of Strata in the Space of Differentials
The Horocycle Flow on Eigenform Loci
Multiple Mixing and Ratner Property in Area-Preserving Flows
The Boundary of an Affine Invariant Submanifold