Minmax minimal surfaces in arbitrary codimension with

Tristan Rivière
ETH Zürich; Member, School of Mathematics
January 29, 2019

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 and whose
Morse index is bounded by the
dimension of the familly. We will discuss the question of bounding the
Morse index + Nullity from below as well as possible extensions of
this procedure to more general families.

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,

(Non)uniqueness questions in mean curvature flow

Lu Wang
University of Wisconsin–Madison; Member, School of Mathematics
January 22, 2019

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 develops singularities
in finite time. In this talk, we discuss some non-uniqueness problems
of the mean curvature flow passing through singularities. The talk is
mainly prepared for non-specialists of geometric flows.