The Zilber-Pink conjecture

Jonathan Pila
University of Oxford
October 26, 2018

The Zilber-Pink conjecture is a far reaching finiteness conjecture in diophantine geometry, unifying and extending Mordell-Lang and Andre-Oort. This lecture will state the conjecture, illustrate its varied faces, and indicate how the point-counting strategy can be applied to parts of it.

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.

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.

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.