Top-level heading

An optimal control approach to Reinforcement Learning

Optimal control and Reinforcement Learning (RL) deal both with sequential decision-making problems, although they use different tools. We have investigated the connection between these two research ar...

The Hermitian geometry of the Chern connection

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...

Uncertainty quantification for traffic flow models via a stochastic Galerkin approach

Although traffic models have been extensively studied, obtaining trustful forecast from these models is still challenging, since the evolution of traffic is also exposed to the presence of uncertainti...

HJB-RBF based approach for the control of PDEs

Semi-lagrangian schemes for discretization of the dynamic programming principle are based on a time discretization projected on a state-space grid. The use of a structured grid makes this approach not...

The Gatenby-Gawlinski model for acid-mediated tumour growth

For evident reasons, Cancer Biology is one of the most challenging topics of current medical research and understanding the mechanism behind its uncontrolled growth is a crucial issue. Among other exp...

Moduli spaces of residueless meromorphic differentials and the KP hierarchy

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...

Horospheres in several complex variables

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 ...

Stochastic Galerkin Formulations for Hyperbolic Balance Laws

The idea to represent stochastic processes by orthogonal polynomials has been employed in uncertainty quantification and inverse problems. This approach is known as stochastic Galerkin formulation wit...

Centers as cohomology, representations and microlocal sheaves

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...