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...
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...
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...
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...
We obtain a finiteness result for the fundamental group of a closed Riemannian manifold
$(M^n,g)$ under the assumption that the Schrödinger operator $\Delta_g+(n-2)/\rho$ is
positive (where at $x\in M...
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...
This is joint work with Peter Feller. In any category there are the following fundamental
problems concerning embeddings from an object Z into another object X:
1. (Existence) Does there exist an embe...
A polynomial functor P is a functor from the category of finite-dimensional vector spaces to itself such that for every U,V the map Hom(U,V) -> Hom(P(U),P(V)) is polynomial. In characteristic zero,...
ecently, Oguiso addressed the following question, attributed to Gizatullin: “Which
automorphisms of a smooth quartic K3 surface $D\subset\mathbb{P}^3$ are induced by
Cremona transformations of the amb...
Let G be a simple algebraic group with flag variety G/B. The Springer resolution is the
moment map from the cotangent bundle of G/B to the (dual of the) Lie algebra g of G. The
cohomology of the fiber...
We address the question of statistical model selection for a class of stochastic models of biological neural nets.Models in this class are systems of interacting chains with memory of variable length....
