As shown by Gromov-Lawson and Stolz the only obstruction to the existence of positive scalar curvature metrics on closed simply connected manifolds in dimensions at least five appears on spin manifold...
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-...
