After reviewing some basic properties of holomorphic Poisson geometry, we will present a decomposition result in the Kähler case: if a compact Kähler Poisson manifold has a compact symplectic leaf wit...
In this talk I will explain how to recognize complex tori among Kähler klt spaces (smooth in codimension 2) in terms of vanishing of Chern numbers. It requires first to define Chern classes on singula...
Kazhdan and Lusztig introduced their eponymous polynomials for a Coxeter group W in 1979. Shortly thereafter, Lascoux and Schuetzenberger studied Kazhdan-Lusztig polynomials for Grassmannians and show...
I will survey on some long-standing open problems and some recent results about the regularity of minimizers of various relaxed energies. I will focus on the model case of harmonic maps from the 3-dim...
Interfacial energy functionals are ubiquitous in nature. However, some of the most basic questions are still open. In this talk, I will address one of these questions and characterize local minimizers...
The interplay between variational functionals and the Brunn-Minkowski Theory is currently a well-established phenomenon that has been widely investigated in the last thirty years. In this talk, we pre...
In this talk we will present some analysis aspects of gauge theory in high dimension. First, we will study the completion of the space of arbitrary smooth bundles and connections under L^p-control of ...
In the talk I will introduce some variational models where an aggregating term, like the perimeter or a Dirichlet-type energy, is in competition with a repulsive one. Examples of such models arise nat...
Weak KAM theory originally connected Mather theory of Lagrangian Systems with Viscosity Theory of the solutions of the corresponding Hamilton-Jacobi Equation, at least when the Hamiltonian is obtained...
We consider the discounted approximation of the critical Hamilton-Jacobi equation set on the real line associated with the Hamiltonian G(x,p):=H(x,p)-V(x), where H is a 1-periodic Tonelli Hamiltonian ...
I will introduce a new heat flow for harmonic maps with free boundary. After giving some motivations to study such maps in relation with extremal metrics in spectral geometry, I will construct weak so...
In 1971 J. Serrin proved that, given a smooth bounded domain Ω⊂Rn and u a positive solution of the problem: −Δu=f(u) in Ω, u=0 on ∂Ω, ∂_νu= constant on ∂Ω, then Ω is necessarily a ball and u is radial...
