The aim of this talk is to give an update on recent achievements and developments on rigid compact complex manifolds. I will start introducing different notions of rigidity and explaining the relation...
I will discuss a criterion for the projectivisation of a reflexive sheaf on a klt space to be induced by a projective representation of the fundamental group of the smooth locus. This criterion is the...
We first review some basic results related to Serre's notion of G-complete reducibility for a reductive algebraic group G. We then discuss a relative variant of this concept where we let K be a reduct...
Given a vector bundle of arbitrary rank with ample determinant line bundle on a projective manifold, we propose a new elliptic system of differential equations of Hermitian-Yang-Mills type for the cur...
In this talk I will give a broad presentation of my research interests which are in the interplay of modeling, analysis and numerical treatment of Partial Differential Equations (PDEs) describing coll...
I will present some recent results concerning highly degenerate elliptic equations of fully nonlinear type. In particular I will speak about the singular Dirichlet problem, the strong maximum principl...
The Brauer group of an algebraic variety X is the group of Azumaya algebras over X, or equivalently the group of Severi-Brauer varieties over X. It is a central object in algebraic and arithmetic geom...
I will give a general overview of the main results concerning existence and qualitative properties of solutions to a family of semilinear elliptic problems involving critical Moser-Trudinger type non-...
This talk will consider several examples of large-scale random systems, such as particles systems with conservation laws, systems of random walks with mutual or self-interaction, the dimer model in Z^...
