BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Lower bounds for the Hodge Laplacian spectrum on non-convex domain
 s - Tirumala Venkata Chakradhar (University of Bristol)
DTSTART:20260205T144500Z
DTEND:20260205T150000Z
UID:TALK239842@talks.cam.ac.uk
DESCRIPTION:The Hodge Laplacian\, which generalises the Laplace-Beltrami o
 perator on smooth functions to the framework of differential forms on Riem
 annian manifolds\, is a central analytic tool in spectral geometry reveali
 ng geometric and topological features of the underlying space through its 
 interaction with homology. In this talk\, we present geometric lower bound
 s for the smallest positive eigenvalue of the Hodge Laplacian in the class
  of non-convex domains given by Euclidean annular regions with a convex ou
 ter boundary and a spherical inner boundary. We also discuss extensions to
  perforated domains in general. The proofs employ local-to-global argument
 s via an explicit isomorphism between Čech cohomology and de Rham cohomol
 ogy to obtain Poincar&eacute\;-type inequalities with explicit geometric d
 ependence\, together with certain generalised versions of the Cheeger-McGo
 wan glueing lemma. This is a joint work with Pierre Guerini.
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR