Video Lectures

The Brunn-Minkowski inequality is a fundamental result in convex geometry controlling the volume of  the sum of subsets of ℝn. It asserts that for  sets A,B⊂ℝn of equal volume and a parameter t∈(0,1), we have |tA+(1−t)B|≥|A| with equality iff A=B is...

Matroids are combinatorial abstractions of the notion of linear independence. They are one of the main objects studied in the current special year in the School of Mathematics. I will talk about a notion of scattering amplitudes for matroids. It is...

Tree decompositions, and in particular path decompositions, are a powerful tool in both structural graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”...

This talk will be about joint work with Fabian Ziltener in which we show that a compact n-rectifiable subset of R^2n with vanishing n-Hausdorff measure can be displaced from itself by a Hamiltonian diffeomorphism arbitrarily close to the identity...

We introduce an SFT-type invariant for Legendrian knots in R^3, which is a deformation of the Chekanov-Eliashberg differential graded algebra. The differential includes components that count index zero pseudoholomorphic disks with up to two positive...

One of the earliest achievements of mirror symmetry was the prediction of genus zero Gromov-Witten invariants for the quintic threefold in terms of period integrals on the mirror. Analogous predictions for open Gromov-Witten invariants in closed...

We prove an effective equidistribution theorem for semisimple

closed orbits on compact adelic quotients. The obtained error depends polynomially on the minimal complexity of intermediate orbits and the complexity of the ambient space. As an...