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# Symplectic non-squeezing for the cubic NLS on R^2

## New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015

October 19, 2015 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Monica Visan (University of California, Los Angeles)
Location: MSRI: Simons Auditorium
Tags/Keywords
• Hamiltonian PDE

• Gromov

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

#### 14370

Abstract

We prove that the flow of the mass-critical NLS in two dimensions cannot squeeze a ball in $L^2$ into a cylinder of lesser radius.  This is a PDE analogue of Gromov's non-squeezing theorem for an infinite-dimensional Hamiltonian PDE in infinite volume.  This is joint work with R. Killip and X. Zhang

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