# Seminars & Colloquia Calendar

## Geodesics revisited

#### Annegret Burtscher - Rutgers University

Location: ** Hill 703**

Date & time: Wednesday, 02 May 2018 at 12:00PM - 1:00PM

Abstract: Geodesics generalize the notion of straight lines to curved spaces. They are curves on a (semi)-Riemannian manifold which solve the geodesic equation, a second order ordinary differential equation. In Riemannian geometry existence and uniqueness of geodesics thus follows from the standard theory for ordinary differential equations (Picard-Lindeloef Theorem). However, this requires the Riemannian metric to be of regularity C^{1,1} or more. If the Riemannian metric has just slightly less regularity the existence of geodesics is still valid but otherwise all hell breaks loose. We will discuss some instructive but little known examples of 2-dimensional Riemannian manifolds that amongst others violate local uniqueness of geodesics and the local length-minimizing property. Some (conjectured) fixes to restore the usual behavior of geodesics also in lower regularity will be discussed at the end.

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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