BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Prof Semyon Dyatlov (MIT)
DTSTART:20210129T150000Z
DTEND:20210129T160000Z
DTSTAMP:20260423T021037Z
UID:OpenPDEA/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OpenPDEA/1/"
 >Control of eigenfunctions on negatively curved surfaces</a>\nby Prof Semy
 on Dyatlov (MIT) as part of Open PDE and analysis seminar and lectures\n\n
 \nAbstract\nGiven an $L^2$-normalized eigenfunction with eigenvalue $\\lam
 bda^2$ on a compact Riemannian manifold $(M\,g)$ and a non-empty open subs
 et $\\Omega$ of $M$\, what lower bound can we prove on the $L^2$-mass of t
 he eigenfunction on $\\Omega$? The unique continuation principle gives a b
 ound for any $\\Omega$ which is exponentially small as $\\lambda$ goes to 
 infinity. On the other hand\, microlocal analysis gives a $\\lambda$-indep
 endent lower bound if $\\Omega$ is large enough\, i.e. it satisfies the ge
 ometric control condition. This talk presents a $\\lambda$-independent low
 er bound for any set $\\Omega$ in the case when $M$ is a negatively curved
  surface\, or more generally a surface with Anosov geodesic flow.  The pro
 of uses microlocal analysis\, the chaotic behaviour of the geodesic flow\,
  and a new ingredient from harmonic analysis called the Fractal Uncertaint
 y Principle. Applications include control for Schrödinger equation and ex
 ponential decay of damped waves.  Joint work with Jean Bourgain\, Long Jin
 \, and Stéphane Nonnenmacher.\n
LOCATION:https://researchseminars.org/talk/OpenPDEA/1/
END:VEVENT
END:VCALENDAR