# Seminars & Colloquia Calendar

## Coisotropic submanifolds of symplectic manifolds, leafwise fixed points, and spherical nonsqueezing

#### Fabian Ziltener, Univ of Utrecht

Location: ** ARC Rm # 203 **

Date & time: Tuesday, 21 January 2020 at 10:00AM - 11:00AM

My talk is partly about joint work with Dusan Joksimovic, and with Jan Swoboda.

Consider a symplectic manifold \((M,\omega)\), a closed coisotropic submanifold \(N\) of \(M\), and a Hamiltonian diffeomorphism \(\phi\) on \(M\). A leafwise fixed point for \(\phi\) is a point \(x\in N\) that under \(\phi\) is mapped to its isotropic leaf. These points generalize fixed points and Lagrangian intersection points. In classical mechanics leafwise fixed points correspond to trajectories that are changed only by a time-shift, when an autonomous mechanical system is perturbed in a time-dependent way.

J. Moser posed the following problem: Find conditions under which leafwise fixed points exist. A special case of this problem is V.I. Arnold's conjecture about fixed points of Hamiltonian diffeomorphisms.

The main result presented in this talk is that leafwise fixed points exist if the Hamiltonian diffeomorphism is the time-1-map of a Hamiltonian flow whose restriction to \(N\) stays \(C^0\)-close to the inclusion \(N\to M\). I will also mention a version of this result that is locally uniform in the symplectic form and the coisotropic submanifold.

As an application of a related result, no neighbourhood of the unit sphere symplectically embeds into the unit symplectic cylinder. This sharpens Gromov's nonsqueezing result.

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

Brooke Logan

Wujun Zhang Organizer's webpage

Ziming Shi, Sagun Chanillo, Xiaojun Huang, Chi Li, Jian Song Seminar website Old seminar website

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

Hong Chen Seminar webpage

Brian Pinsky, Rashmika Goswami website

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

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