In this talk, I will give an overview on how PCPs, combined with
cryptographic tools, are used to generate succinct and efficiently
verifiable proofs for the correctness of computations. I will focus
on constructing (computationally sound)...
Mean curvature flow is the negative gradient flow of the volume
functional which decreases the volume of (hyper)surfaces in the
steepest way. Starting from any closed surface, the flow exists
uniquely for a short period of time, but always...
In this talk I would like to explain how methods from symplectic
geometry can be used to obtain sharp systolic inequalities. I will
focus on two applications. The first is the proof of a conjecture
due to Babenko-Balacheff on the local...
What is the largest number of projections onto k coordinates
guaranteed in every family of m binary vectors of length n? This
fundamental question is intimately connected to important topics
and results in combinatorics and computer science (Turan...
The lecture will discuss recent joint work with C. Bellettini and
O. Chodosh. The work taken together establishes sharp regularity
conclusions, compactness and curvature estimates for any family of
codimension 1 integral $n$-varifolds satisfying: (i...
In their seminal works from the 80's, Lubotzky, Phillips and
Sarnak proved the following two results: (i) An explicit
construction of Ramanujan regular graphs. (ii) An explicit method
of placing points on the sphere uniformly equidistributed...
Motivated by questions in computer science, we consider the problem
of approximating local points (real or p-adic points) on the unit
sphere S^d optimally by the projection of the integral points lying
on R*S^d, where R^2 is an integer. We present...
Renormalized volume (and more generally W-volume) is a geometric
quantity found by volume regularization. In this talk I'll describe
its properties for hyperbolic 3-manifolds, as well as discuss
techniques to prove optimality results.
