We discuss a novel class of swarm-based gradient descent (SBGD) methods for non-convex optimization. The swarm consists of agents, each is identified with position, x, and mass, m. There are three key...
We produce complete, non-compact, Riemannian metrics with positive constant \sigma_2-curvature on a sphere of dimension n>4, with a prescribed singular set given by a disjoint union of closed subma...
We study the surface diffusion flow in the flat torus, that is, smooth hypersurfaces moving with the outer normal velocity given by the Laplacian of their mean curvature. This model describes the evol...
Abstract: This talk provides an overview of my research interests which rely on the theoretical and computational aspects of optimal control problems, with a particular emphasis on the Hamilton-J...
Abstract: In this talk we will review some recent results on the Fröhlich polaron, which is a model for a charged particle coupled to a polarizable medium. We will especially focus on a conjecture due...
SOL is one of Thurston's eight classical homogeneous Riemannian geometries, possibly the most exotic one. To get some insight of this geometry, it might be helpful to visualize the shape of a large sp...
We introduce a general framework for the study of numerical approximations of a certain class of solutions, called stable solutions, of second order mean-field game systems for which uniqueness of sol...
We consider a family of processes obtained by decomposing the deterministic dynamics associated with some fluid models (e.g. Lorenz 96, 2d Galerkin-Navier-Stokes) into fundamental building blocks - i....
In this talk, we present a general existence result to the problem of prescribing curvatures on a disk under conformal changes of the metric. We treat the case of negative Gaussian curvature, as a fir...
