On several types of fractals, it is possible to build a Dirichlet form in a natural way; it is also possible to define a dynamical system and we shall see that the Dirichlet form has a natural relatio...
The aim of this course is to present some recent advances in the theory of stable sheaves on higher dimensional varieties, in particular Fano and hyper-Kähler manifolds. We will start by reviewing the...
In this talk, we use an enhanced Lyapunov-Schmidt reduction method to study a specific class of nonlinear Schrödinger systems with sublinear coupling terms. We establish the existence of infinitely ma...
Cluster algebras of type A are subalgebras of a field of rational functions in several variables. They are generated by a distinguished set of generators, the cluster variables, which correspond to th...
We present some results for Radon measure-valued solutions of first order scalar conservation laws. In particular we discuss the case in which the singular part of the initial datum is a superposition...
We study some qualitative properties of the solutions to a segregation limit problem in planar domains. The main goal is to show that, generically, the limit configuration of N competing populations c...
Magnetic systems are the natural toy model for the motion of a charged particle moving on a Riemannian manifold under the influence of a (static) magnetic force. In this talk we introduce a curvature ...
K-stability (or existence of Kähler-Einstein metrics) of explicit Fano varieties has been studied for a long time. Delta invariants (stability thresholds) detect the K-stability of Fano varieties. Mor...
Let \( G \) be a finite group. It is not hard to see that for any representation \( \rho: G \to \mathrm{GL}(V) \) for \( V \) a real vector space, there exists a \( G \)-invariant bilinear form \( \be...
It is known by the works of Adamović and Perše that the affine simple vertex algebras associated with G2 and B3 at level -2 can be conformally embedded into \( L_{-2}(D4). \) In this talk, I will pre...
