Abstract: (i) A powerful tool in regularity theory for PDEs is given by representation formulas: your solution is expressed by the convolution of the data of the equation with a kernel with known (goo...
We explain our recent work on the classification of surfaces of general type with p_g=q=2 or p_g=q=1. Our approach is based on cohomological rank functions, the Chen-Jiang decomposition/Fujita decompo...
Chen-Gounelas-Liedtke recently introduced a powerful regeneration technique, a process opposite to specialization, to prove existence results for rational curves on projective K3 surfaces. In the talk...
In questo contributo si presenteranno alcuni risultati di un progetto di ricerca internazionale (IDENTITIES) sul tema dell'educazione all'interdisciplinarità tra matematica e fisica nella scuola secon...
I will survey some results from the study of moduli spaces of higher dimensional varieties as well as the Hassett—Keel program for the moduli space of curves. I will then discuss applications of these...
In this talk I will discuss some results about long time behaviors of solutions to Hamiltonian PDEs (Schrödinger, Kirchhoff, etc). In particular I will focus on a recent result where we (with J. Berni...
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...
A fascinating aspect of collective dynamics is self-organization of small-scale interactions into high-order structures with larger-scale patterns. In different contexts these are clusters which take ...
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...
