I will discuss geometric and dynamical properties of actions of discrete groups on Riemannian symmetric spaces. I will highlight some aspects of the interplay between geometry and dynamics, and presen...
We consider some problems concerning the geometry of the Chern connection, including: metrics with constant Chern-scalar curvature; the generalizations of the Kähler-Einstein condition to the non-Kähl...
I'll present a recent joint work with A. Buryak and D. Zvonkine, where we study the moduli spaces of residueless meromorphic differentials, i.e., the closures, in the moduli space of stable curves, of...
A horocycle in the unit disk of the complex plane is a euclidean disk which is internally tangent to a point p of the boundary of the disk. Horocycles are limits of Poincaré balls as the center moves ...
This is a joint work with G. Courtois, S. Gallot and A. Sambusetti. We shall prove that, given two positive numbers and H, there are finitely non cyclic torsion-free -hyperbolic marked groups (Γ.Σ) sa...
In a pioneering 1981 paper De Concini and Procesi provided a beautiful description for cohomology of fixed point sets (Springer fibers) (G/B)_ϵ in type A. This was an important precursor to two later...
The Chern character is a central construction which appears in topology, representation
theory and algebraic geometry.
In algebraic topology it is for instance used to probe algebraic K-theory which i...
The theory of conformal blocks provides us with projective representations of the mapping
class group. These can equivalently also be constructed from the point of view of
non-abelian theta functions,...
Quasi-fibered boundary metrics (QFB metrics) form a class of complete metrics generalizing
the class of quasi-asymptotically locally Euclidean metrics introduced by Joyce.
After reviewing what QFB met...
A key tool to study the plane Cremona group is its action on a hyperbolic space. Sadly, in higher rank such an action is not available. Recently, in geometric group theory, actions on CAT(0) cube comp...
In higher Teichmuller theory we study subsets of the character varieties of surface groups that are higher rank analogs of Teichmuller spaces, e.g. the Hitchin components and the spaces of maximal rep...
