Video Lectures

We prove the existence of subspace designs with any given parameters, provided that the dimension of the underlying space is sufficiently large in terms of the other parameters of the design and satisfies the obvious necessary divisibility...

Contact homology is a Floer-type invariant for contact manifolds, and is a part of Symplectic Field Theory. One of its first applications was the existence of exotic contact structures on spheres. Originally, contact homology was defined only for...

The Zimmer program asks how lattices in higher rank semisimple Lie groups may act smoothly on compact manifolds. Below a certain critical dimension, the recent proof of the Zimmer conjecture by Brown-Fisher-Hurtado asserts that, for SL(n,R) with n...

Erdős' unit distance problem and his related distinct distances problem are arguably the best known open problems in discrete geometry.

They ask for the maximum possible number of unit distances, and the minimum possible number of distinct...

Statistical mechanics models undergoing a phase transition often exhibit rich, fractal-like behaviour at their critical points, which are described in part by critical exponents, the indices governing the power-law growth or decay of various...

The Loewner energy is a Möbius invariant quantity that measures the roundness of Jordan curves on the Riemann sphere. It arises from large deviation deviations of SLE0+ and is also a Kähler potential on the Weil-Petersson Teichmüller space...

Donaldson-Thomas (DT) invariants of a quiver with potential can be expressed in terms of simpler attractor DT invariants by a universal formula. The coefficients in this formula are calculated combinatorially using attractor flow trees. In joint...

This lecture is devoted to a survey on explicit stability results in Gagliardo-Nirenberg-Sobolev and logarithmic Sobolev inequalities. Generalized entropy methods based on carré du champ computations and nonlinear diffusion flows can be used for...

In 1996 Manjul Barghava introduced a notion of P-orderings for arbitrary sets S of a Dedekind domain, with respect to a prime ideal P, which defined associated invariants called P-sequences. He combined these invariants to define generalized...