In this talk we present some recent results on the convergence of nonlinear Dirichlet problems for systems of variational elliptic PDEs defined on randomly perforated domains of Rn. Under the assumpti...
We discuss in two relevant case-studies the rigorous derivation via Gamma-convergence of asymptotic energies accounting for singularities in elastic materials from non-local models (convolution-type i...
This mini-course is concerned with those PDEs which have a gradient flow structure in the Wasserstein space W_2 and can thus be attacked via the so-called Jordan-Kinerlehrer-Otto scheme, a sequence of...
Nonlocal shape optimization problems involving interaction energies with competing repulsive and attractive terms are of interest in a variety of applications and have been extensively studied in the ...
Over the recent years deterministic interacting-particle approximations of gradient flows in Wasserstein and other geometries have gained popularity in applications to machine learning and other areas...
When quantum fields are represented as operators on a Hilbert space, their two-point distributions naturally give rise to distributions of positive type. A number of basic results on such distributi...
We present a new Mountain Pass Theorem for a class of functionals that depends on two arguments which only partially satisfies the Palais-Smale condition. This abstract functional setup will be a...
The Dynamical Manin-Mumford problem is a dynamical question inspired by classical results from arithmetic geometry. Given an algebraic dynamical system (X,f), where X is a projective variety and f is ...
Classical q-shuffle algebras provide combinatorial models for the positive half U_q(n) of a finite quantum group. We define a loop version of this construction, yielding a combinatorial model for the...
We will introduce and discuss a notion of s-fractional mass for 1-currents, generalizing the s-fractional perimeter in the plane to higher codimension singularities. We will present basic compactn...
