We shall present a procedure which to any admissible family of
immersions of surfaces into an arbitrary closed riemannian
manifolds assigns a smooth, possibly branched, minimal surface
whose area is equal to the width of the corresponding minmax...
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...
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...
