Title: Frobenius-type results on submanifolds and currentsAbstract: The question of producing a foliation of the n-dimensional Euclidean space with k-dimensional submanifolds which are tangent to a prescribed k-dimensional simple vectorfield is part of the celebrated Frobenius theorem: a decomposition in smooth submanifolds tangent to a given vectorfield is feasible (and then the vectorfield itself is […]
Title: Highly Connected 7-manifolds, Non-negative Curvature and the Linking FormAbstract: Closed manifolds admitting non-negative sectional curvature are not very well understood and it is, at present, quite difficult to obtain examples with interesting topology. All known examples depend in some way on two basic facts: First, compact Lie groups admit a bi-invariant metric (hence, non-negative […]
Title: A non-Archimedean characterization of local K-stability.Abstract: Log Fano cone singularities are generalizations of affine cones over Fano varieties. Motivated by the study of canonical metrics on Fano varieties, there is a local K-stability theory characterizing the existence of Ricci-flat K"ahler cone metrics on log Fano cone singularities. In this talk, we aim to give a non-Archimedean […]
Title: Fourier Interpolation and the Weil Representation Abstract: In 2017, Radchenko-Viazovska proved a remarkable interpolation result for even Schwartz functions on the real line: such a function is entirely determined by its values and those of its Fourier transform at square roots of integers. We give a new proof of this result, exploiting the fact […]
Title: Springer resolution and representation theoryAbstract: Given a connected complex reductive group G, I would like to explain how doing geometry on the Springer resolution and the Steinberg variety allows one to give a spectral description (i.e. irreducible representations) of the Weyl group of G.