# Seminars & Colloquia Calendar

## Flat and hyperbolic geometry of surfaces

#### James Farre (Yale)

Location: ** Hill 705**

Date & time: Tuesday, 11 February 2020 at 3:50PM - 4:40PM

The uniformization theorem tells us that the deformation space of constant curvature metrics on a surface also describes the moduli space of its complex structures. We will review some constructions coming from hyperbolic geometry and some coming from complex analysis. Using Bonahon and Thurston’s shear coordinates for Teichmüller space, Mirzakhani proved that two flows, namely earthquake flow from hyperbolic geometry and Teichmüller horocycle flow from complex analysis, are measurably isomorphic. Mirzakhani’s correspondence does not factor through uniformization and it is defined only on a measurably generic set. We will introduce a new coordinate system for Teichmüller space that allows us to extend Mirzakhani’s conjugacy everywhere in a natural way relating the hyperbolic geometry of a surface to certain singular flat metrics induced by quadratic differentials. This is joint work (in progress) with Aaron Calderon.

R. Shapiro Organizer's Page

Chiara Damiolini, Ian Coley and Franco Rota -Charles Weibel Organizer's Page

Brooke Logan

Wujun Zhang Organizer's webpage

P. Gupta, X.Huang and J. Song Organizer's webpage

Swastik Kopparty, Sepehr Assadi Seminar webpage

Jeffry Kahn, Bhargav Narayanan, Jinyoung Park Organizer's webpage

Brooke Ogrodnik, Website

Robert Dougherty-Bliss and Doron Zeilberger --> homepage

Paul Feehan, Daniel Ketover, Natasa Sesum Organizer's webpage

Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward Organizer's webpage

Jason Saied Seminar webpage

Brian Pinsky, Rashmika Goswami website

Quentin Dubroff Organizer's webpage

James Holland; Organizer website

Edna Jones Organizer's webpage

Brooke Ogrodnik website

Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum Organizer's Webpage

Organizer: Luochen Zhao

Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song Organizer's Page

Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's webpage

Simon Thomas website

Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page

Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis Organizer's Webpage

Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Alex Walker seminar website

Stephen D. Miller

Brooke Ogrodnik, Website

Organizers: Yanyan Li, Z.C. Han, Jian Song, Natasa Sesum

Yael Davidov Seminar webpage

Kristen Hendricks, Xiaochun Rong, Hongbin Sun, Chenxi Wu Organizer's page

Fioralba Cakoni Seminar webpage

Ebru Toprak, Organizer

Organizer's webpage: Organizer's webpage

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