Geometry & Analysis Seminar Fall 2019

Wednesdays - 2:45pm
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


Wednesday October 23rd, 2019

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


Wednesday October 30th, 2019

TBA


Wednesday November 6th, 2019

TBA


Wednesday November 13th, 2019

TBA


Wednesday November 20th, 2019

TBA


Wednesday November 27th, 2019

TBA


Wednesday December 4th, 2019

TBA 


Wednesday December 11th, 2019

Zhen Huang, City University of New York