The aim of this course is to present some recent advances in the theory of stable sheaves on higher dimensional hyper-Kähler manifolds. In the first part we will review Mukai's theory on K3 surfaces. ...
We consider radial solutions of fully nonlinear, uniformly elliptic equations posed in punctured balls, in presence of radial singular quadratic potentials. We discuss both the principal eigenvalues p...
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 ...
Tannaka Duality refers to the reconstruction of a compact group from its representations, while Serre's GAGA theorem relates coherent sheaves on an algebraic variety to its analytification. This talk...
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...
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...
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...
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...
Aeppli and Bott-Chern cohomologies are useful invariants on compact complex manifolds, especially if they do not admit Kahler metrics. In this seminar we will introduce generalisations of these object...
The principle behind magnetic fusion is to confine high temperature plasma inside a device in such a way that the nuclei of deuterium and tritium joining together can release energy. The high temperat...
