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...
The Margulis Lemma states that in a hyperbolic manifold, the subgroup of the fundamental group generated by small loops around a certain point behaves like an abelian group (more precisely, it is virt...
Abstract: Stationary non equilibrium states (SNS) have a rich and complex structure. The large deviations rate functionals for the empirical measure of a few one dimensional SNS of stochastic interact...
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...
Abstract: Neurophysiologists are nowadays able to record from a large number of extracellular electrodes and to extract, from the raw data, the sequences of action potentials or spikes generated by ma...
The correlation energy of a high density fermionic Coulomb gas, called Jellium, is expected to be given by the Gell-Mann Brueckner formula. I will discuss an analogue of this formula for the mean-fiel...
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 ...
Given a projective complex manifold M with an ample polarization there is canonically associated an affine bundle Z over M. The question I will discuss is under which circumstances Z is an affine vari...
We present a study of spectral gaps, entropy production and log Sobolev inequalities for some Lindblad equations modeling systems of N particles interacting pairwise. The bounds obtained, some o...
