Video Lectures

Abstract: After recalling the gluing construction for Kaehler constant scalar curvature and extremal (`a la Calabi) metrics starting from a compact or ALE orbifolds with isolated singularities, I will show how to compute the Futaki invariant of...

Abstract: We discuss singularities of Teichmueller harmonic map flow, which is a geometric flow that changes maps from surfaces into branched minimal immersions, and explain in particular how winding singularities of the map component can lead to...

The emerging theory of High-Dimensional Expansion suggests a number of inherently different notions to quantify expansion of simplicial complexes. We will talk about the notion of local spectral expansion, that plays a key role in recent advances in...

Abstract: Given a class of conformally compact Einstein manifolds with boundary, we are interested to study the compactness of the class under some local and non-local boundary constraints. I will report some joint work with Yuxin Ge and Jie Qing...

In this talk we discuss the cubic wave equation in three dimensions. In three dimensions the critical Sobolev exponent is 1/2. There is no known conserved quantity that controls this norm. We prove unconditional global well-posedness for radial...

Geodesic nets on Riemannian manifolds is a natural generalization of geodesics. Yet almost nothing is known about their classification or general properties even when the ambient Riemannian manifold is the Euclidean plane or the round 2-sphere.

In...

Positive geometries are real semialgebraic sets inside complex varieties characterized by the existence of a meromorphic top-form called the canonical form. The defining property of positive geometries and their canonical forms is that the residue...

A matroid is an abstract combinatorial object which generalizes the notions of spanning trees, and linearly independent sets of vectors. I will talk about an efficient algorithm based on the Markov Chain Monte Carlo technique to approximately...