Irreducible components of affine Deligne-Lusztig varieties and orbital integrals

Rong Zhou
Member, School of Mathematics
October 25, 2018
Affine Deligne-Lusztig varieties (ADLV) naturally arise in the study of Shimura varieties and Rapoport-Zink spaces; their irreducible components give rise to interesting algebraic cycles on the special fiber of Shimura varieties. We prove a conjecture of Miaofen Chen and Xinwen Zhu, which relates the number of irreducible components of ADLV's to a certain weight multiplicity for a representation of the Langlands dual group.

Existence of infinitely many minimal hypersurfaces in closed manifolds

Antoine Song
Princeton University
October 23, 2018
In the early 80’s, Yau conjectured that in any closed 3-manifold there should be infinitely many minimal surfaces. I will review previous contributions to the question and present a proof of the conjecture, which builds on min-max methods developed by F. C. Marques and A. Neves. A key step is the construction by min-max theory of a sequence of closed minimal surfaces in a manifold N with non-empty stable boundary, and I will explain how to achieve this via the construction of a non-compact cylindrical manifold.

New Results in Tests of Gravity with Radio Pulsars

Michael Kramer
Max Planck Institute for Radio Astronomy
October 23, 2018

We are living in a golden era for testing gravitational physics with precision experiments. This talk will present new results using a variety of tests with radio pulsars. These results will be placed in context of other experiments (including LIGO, EHT etc), and I will demonstrate how pulsars continue to provide unique constraints on gravity and fundamental physics in general, and how they complement other methods.

Small-Set Expansion on the Grassmann Graph.

Dor Minzer
Member, School of Mathematics
October 23, 2018
A graph G is called a small set expander if any small set of vertices contains only a small fraction of the edges adjacent to it.
This talk is mainly concerned with the investigation of small set expansion on the Grassmann Graphs, a study that was motivated by recent applications to Probabilistically Checkable Proofs and hardness of approximation.

Approximating the edit distance to within a constant factor in truly subquadratic time.

Mike Saks
Rutgers University
October 22, 2018
Edit distance is a widely used measure of similarity of two strings based on the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. The edit distance can be computed exactly using a classical dynamic programming algorithm that runs in quadratic time.

New and old results in the classical theory of minimal and constant mean curvature surfaces in Euclidean 3-space R^3

Bill Meeks
University of Massachusetts Amherst
October 22, 2018
In this talk I will present a survey of some of the famous results and examples in the classical theory of minimal and constant mean curvature surfaces in R^3. The first examples of minimal surfaces were found by Euler (catenoid) around 1741, Muesner (helicoid) around 1746 and Riemann (Riemann minimal examples) around 1860. The classical examples of non-zero constant mean curvature surfaces are the Delaunay surfaces of revolution found in 1841, which include round spheres and cylinders.