Tuesday, July 30, 2019
Time  Items 

All day 

10am 
07/30/2019  10:00am We prove an inequality conjectured by Larry Guth that relates the mdimensional Hausdorff content of a compact metric space with its (m − 1) dimensional Urysohn width. As a corollary, we obtain new systolic inequalities that both strengthen the classical Gromov’s systolic inequality for essential Riemannian manifolds and extend this inequality to a wider class of nonsimply connected manifolds. We also present a new version of isoperimetric inequality. It asserts that for every positive integer m, Banach space B, compact subset X of B, and a closed subset Y of X there is a filling of Y by a continuous image of X with the (m + 1)dimensional Hausdorff content bounded in terms of the mdimensional Hausdorff content of Y. Joint work with Yevgeny Liokumovich, Boris Lishak and Regina Rotman. Location:
LOM 206

1pm 
07/30/2019  1:00pm In 2002 my coauthors and I proved that the familiar double bubble is the leastperimeter way to enclose and separate two given volumes in R^3. In 2008 Ben Reichardt extended the result to R^n. After ten years of no further progress, Milman and Neeman have announced an extension to Gauss space (R^n with Gaussian density). Their work applies not just to double bubbles but to all multiple bubbles in dimensions high enough to easily accommodate them. Although the proof is difficult, the solution and some of the main ideas are easy to describe. We’ll also discuss some open questions and recent results for other densities.
Location:
LOM 206

4pm 
07/30/2019  4:00pm Many examples of sequences which compare and contrast various notions of convergence, including intrinsic flat convergence, will be discussed. Along the way, theorems which were inspired by these examples, relating these notions of convergence, will be introduced. Joint work with Edward Bryden and Christina Sormani will be discussed. Location:
LOM 206
