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.
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...
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...
We prove that the systole (or more generally, any k-th homology
systole) of a minimal surface in an ambient three manifold of
positive Ricci curvature tends to zero as the genus of the minimal
surfaces becomes unbounded. This is joint work...
Given an arbitrary graph, we show that if we are allowed to
modify (say) 1% of the edges then it is possible to obtain a much
smaller regular partition than in Szemeredi's original proof of the
regularity lemma. Moreover, we show that it is...
In this survey talk, I will review the known constructions of
mathematical theories of gauged sigma model and its relations with
Gromov--Witten theory and FJRW theory. I will emphasize the
analytic side, but will also mention related algebraic...
We show that every complete Riemannian manifold of finite volume
contains a complete embedded minimal hypersurface of finite volume.
This is a joint work with Gregory Chambers.
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...
