School of Mathematics

Near-Optimal Strong Dispersers

Dean Doron
The University of Texas at Austin
February 4, 2019

Randomness dispersers are an important tool in the theory of pseudorandomness, with numerous applications. In this talk, we will consider one-bit strong dispersers and show their connection to erasure list-decodable codes and Ramsey graphs. 

Analyticity results for the Navier-Stokes Equations

Guher Camliyurt
Member, School of Mathematics
January 31, 2019
We consider the Navier–Stokes equations posed on the half space, with Dirichlet boundary conditions. We give a direct energy based proof for the instantaneous space-time analyticity and Gevrey class regularity of the solutions, uniformly up to the boundary of the half space. We then discuss the adaptation of the same method for bounded domains.

Upper bounds for constant slope p-adic families of modular forms

John Bergdall
Bryn Mawr College
January 31, 2019
This talk is concerned with the radius of convergence of p-adic families of modular forms --- q-series over a p-adic disc whose specialization to certain integer points is the q-expansion of a classical Hecke eigenform of level p. Numerical experiments by Gouvêa and Mazur in the nineties predicted the general existence of such families but also suggested, in spirit, the radius of convergence in terms of an initial member. Buzzard and Calegari showed, ten years later, that the Gouvêa--Mazur prediction was false. It has since remained open question how to salvage it.

PCP and Delegating Computation: A Love Story.

Yael Tauman Kalai
Microsoft Research
January 28, 2019

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) *succinct* proofs that are *non-interactive*
(assuming the existence of public parameters) and are *publicly verifiable*.
In particular, I will focus on a recent result with Omer Paneth and Lisa Yang,
where we show how to construct such proofs for all polynomial time computations,

New Results on Projections

Guy Moshkovitz
Member, School of Mathematics
January 22, 2019

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 number, Sauer-Shelah Lemma, Kahn-Kalai-Linial Theorem, and more), and is wide open for most settings of the parameters. We essentially settle the question for linear k and sub-exponential m. 

Based on joint work with Noga Alon and Noam Solomon.

Symplectic methods for sharp systolic inequalities

Umberto Hryniewicz
Universidade Federal do Rio de Janeiro; Member, School of Mathematics
January 22, 2019

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 systolic maximality
of the round 2-sphere. The second is the proof of a perturbative
version of Viterbo's conjecture on the systolic ratio of convex energy
levels. If time permits I will also explain how to show that general
systolic inequalities do not exist in contact geometry. Joint work