SMS scnews item created by Daniel Daners at Sun 30 Dec 2012 0918
Type: Seminar
Distribution: World
Expiry: 4 Jan 2013
Calendar1: 4 Jan 2013 1400-1500
CalLoc1: AGR Carslaw 829
Auth: daners@d220-237-41-227.mas801.nsw.optusnet.com.au (ddan2237) in SMS-WASM

PDE Seminar

Analytical aspects of isospectral gongs and drums

Kennedy

James Kennedy
University of Ulm, Germany
4th January 2013 14:05-14:55, Carslaw Room 829 (AGR)

Abstract

Almost 50 years ago, Kac posed the now-famous question Can one hear the shape of a drum?, that is, if two planar domains are isospectral with respect to the Dirichlet (or Neumann) Laplacian, must they necessarily be congruent? This question was answered in the negative about 20 years ago with the construction of pairs of polygonal domains with special group-theoretically motivated symmetries, which are simultaneously Dirichlet and Neumann isospectral.

We wish to revisit these examples from an analytical perspective, recasting the arguments in terms of elliptic forms and intertwining operators. This allows us to prove in particular that the isospectrality property holds for a far more general class of elliptic operators than the Laplacian, as it depends purely on what the intertwining operator does to the form domains. We also show that the same type of intertwining operator cannot intertwine the Robin Laplacian on such domains.

This is joint work with Wolfgang Arendt (Ulm) and Tom ter Elst (Auckland).

Check also the PDE Seminar page. Enquiries to Florica CÓrstea or Daniel Daners.


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