# Past Events

The Nash-Kuiper embedding theorem is a prototypical example of a counter-intuitive approximation result: any short embedding of a Riemannian manifold into Euclidean space can be approximated by isometric ones. As a consequence, any surface can be isometrically C^1-embedded into an arbitrarily…

A corollary in a well-known 1985 article by Uhlenbeck asserts that the W^{1,p}-distance between the gauge-equivalence class of a connection A and the moduli subspace of flat connections, M(P), on a principal G-bundle P over a closed Riemannian manifold X of dimension d<= 2 is bounded by a…

In this talk I will give a brief introduction to slope stability and present a combinatorial criterion for the tangent bundle on a polarised toric variety to be stable in terms of the lattice polytope corresponding to the polarisation. I will then give some applications to toric surfaces and…

A Calabi-Yau (CY) pair (X,D) consists of a normal projective variety and a reduced anti-canonical integral divisor on it. Such pairs arise in a number of contexts; for example, cluster varieties are obtained by gluing CY pairs by volume preserving or crepant birational maps. A CY pair has…