BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Spectral inequalities for the Laplacian on manifolds with bounded 
 sectional curvature - Jean Lagacé (King's College London)
DTSTART:20260209T143000Z
DTEND:20260209T153000Z
UID:TALK244522@talks.cam.ac.uk
DESCRIPTION:A spectral inequality for a set $\\omega$ tells us quantitativ
 ely how small (linear combinations of) eigenfunctions can be on $\\omega$.
  In many settings\, it is known that a spectral inequality holding for $\\
 omega$ is equivalent to $\\omega$ being thick\, which a notion of uniformi
 ty.&nbsp\;\n&nbsp\;\nFor manifolds\, it was shown by Deleporte and Rouveyr
 ol that a subset $\\omega$ of a manifold with Ricci curvature bounded belo
 w can only support a spectral inequality if it is thick. Using a quantitat
 ive unique continuation result for the gradient of a harmonic function due
  to Logunov and Malinnikova\, we show that on manifolds with bounded secti
 onal curvature\, any thick $\\omega$ supports a spectral inequality. Cruci
 ally\, this holds even for manifolds whose injectivity radius goes to zero
 . I will discuss how this hypothesis came to be removed\, and how one may 
 try to match the curvature conditions.\n&nbsp\;\nJoint work with A. Delepo
 rte (Paris-Saclay) and M. Rouveyrol (Bielefeld)
LOCATION:Seminar Room 2\, Newton Institute
END:VEVENT
END:VCALENDAR