# Geometry & Analysis Seminar Fall 2019

McHenry Library Room 4130

For further information please contact Professor Francois Monard or call 831-459-2400

**Wednesday, October 9th, 2019**

**Thibault Lefeuvre, Paris-Sud University/MSRI**

**Geodesic stretch, pressure metric and the marked length spectrum rigidity conjecture**

In 1985, Burns and Katok conjectured that the marked length spectrum of a negatively-curved Riemannian manifold (namely the collection of lengths of closed geodesics marked by the free homotopy of the manifold) should determine the metric up to isometries. This conjecture was independently proved for surfaces in 1990 by Croke and Otal but since then little progress has been accomplished in higher dimensions until our recent proof of the local version of the conjecture, obtained in collaboration with C. Guillarmou. Considering a geometric point of view in the moduli space of isometry classes, I will explain a new proof of this local version of the conjecture which relies on the notion of geodesic stretch. If time permits, I will show that this fits into a more general framework which generalizes Thurston's distance and the pressure metric (initially defined on Teichmuller space) to the setting of variable curvature and higher dimensions. Joint work with C. Guillarmou, G. Knieper.

**Wednesday, October 16th, 2019 @ 2:45PM**

**Ruobing Zhang, Stony Brook University**

**Geometric analysis of collapsing Calabi-Yau spaces**

This talk centers on the degenerations of Calabi-Yau manifolds, particularly on the interactions between algebraic degenerations and metric convergence in the collapsed contexts, which is a long standing question. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties and highly non-algebraic features. As motivating examples, we will also describe our recent results on the new collapsing mechanisms of K3 surfaces. The main part of the lecture is to explain the recent progress in higher dimensions.

**Wednesday, October 16th, 2019 @ 4PM**

**Stephen Kleene, University of Rochester**

*Desingularizing Non-Degenerate Surfaces*

I will discuss recent progress in singular perturbation from the point of view of the Cauchy data operator in the highly symmetric setting. In particular, we will show how to desingularize a generic highly symmetric compact surface satisfying a mean curvature type equation with a transversal self intersection.

**Wednesday, October 23rd, 2019**

**Hadrian Quan, University of Illinois at Urbana-Champaign / MSRI**

*The Heat Kernel of a Contact Manifold in the Sub-Riemannian Limit*

In this talk I will report on joint work with Pierre Albin in which we study the limits of heat kernels on contact manifolds corresponding to a Riemannian metric degenerating to a submetric of the contact structure. This question is approached using the tools of geometric microlocal analysis. Time permitting, I will discuss connections with the Rumin complex, and the associated limit of Analytic Torsion.

**Wednesday, October 30th, 2019**

**TBA**

**Wednesday, November 6th, 2019**

**TBA**

**Wednesday, November 13th, 2019**

**TBA**

**Wednesday, November 20th, 2019**

**Zhen Huang, City University of New York**

**Blowing Up Closed Minimal Surfaces In Hyperbolic Three-Manifolds**

In the late 70s, Uhlenbeck proposed a program to study the moduli space of minimal immersions of closed surfaces in hyperbolic 3-manifolds. This program addresses questions on existence, multiplicity and asymptotic behavior of such immersions. I will present several results in these directions, based on joint work with M. Lucia and G. Tarantello.

**Wednesday, November 27th, 2019**

**TBA**

**Wednesday, December 4th, 2019**

**TBA**

**Wednesday, December 11th, 2019**

**TBA**