Thursday September 27, 2018 2:30 PM  03:30 AM P131
 Boris Bukh, Carnegie Mellon University
Nearly orthogonal vectorsHow can d+k vectors in R^d be arranged so that they are as close to orthogonal as possible? We show intimate connection of this problem to the problem of equiangular lines, and to the problem of bounding the first moment of isotropic measures. Using these connections, we pin down the answer precisely for several values of k and establish asymptotics for all k. Joint work with Chris Cox.

Thursday October 04, 2018 2:30 PM P131
 Nicholas Edelen, MIT
Effective Reifenberg theorems for measuresThe Jones' $β$numbers quantify how ``linear'' is the support of a measure. These have important uses in singularity analysis of solutions to PDE and harmonic analysis. In this talk, I explain joint work with Aaron Naber and Daniele Valtorta which gives quantitative control and Lipschitz structure on measures satisfying natural conditions on the $β$numbers, and generalizations of our results to infinitedimensional spaces. Our work can be viewed as an ``analyst's travelingsalesman'' type theorem.

Thursday October 18, 2018 2:30 PM P131
 Matthew Badger, University of Connecticut
Traveling along Hölder curvesOne goal of geometric measure theory is to understand a measure through its interaction with canonical lower dimension sets. The interaction of Radon measures in the plane or a higherdimensional Euclidean space with finite sets or rectifiable curves is now completely understood. However, with respect to any other elementary family of sets, we only know how measures behave under additional regularity hypotheses. To make progress towards understanding the structure of Radon measures, we need to first understand the geometry of more classes of sets.
I will describe my latest work with L. Naples and V. Vellis, in which we find sufficient conditions to identify (subsets of) Hölder continuous curves of Hausdorff dimension $s>1$. Our conditions are related to the Analyst's Traveling Salesman Theorem, which characterizes subsets of rectifiable curves. On the other hand, standard selfsimilar sets such as the Sierpinski carpet show that our sufficient condition is not necessary. I will discuss this and other obstructions to the problem of characterizing Hölder curves and their subsets.

Thursday October 25, 2018 2:30 PM P131
 Philippe Sosoe, Cornell University
A sharp transition for Gibbs measures
associated to the nonlinear Schroedinger equationIn 1987, Lebowitz, Rose and Speer (LRS) showed how to
construct formally invariant measures for the nonlinear Schroedinger
equation on the torus. This seminal contribution spurred a large amount
of activity in the area of partial differential equations with random
initial data. In this talk, I will explain LRS's result, and discuss a
sharp transition in the construction of the Gibbstype invariant
measures considered by these authors. (Joint work with Tadahiro Oh and
Leonardo Tolomeo)

Thursday November 15, 2018 2:30 PM P131
 Vyron Vellis, University of Connecticut
Quasisymmetric uniformization of metric spheresOne of the biggest problems in Quasiconformal Analysis is the classification of metric spaces which are quasisymmetric (or quasiconformal) to the unit sphere $\mathbb{S}^n$. While settled for $n=1$, the problem is completely open for $n ≥ 2$. In this talk we present a survey on this question and some recent results regarding on how bad (geometrically and analytically) quasisymmetric spheres can be and, similarly, how good nonquasisymmetric spheres can be.

