Liu Bie Ju Centre for Mathematical Sciences
City University of Hong Kong
Mathematical Analysis and its Applications
Colloquium

Organized by Prof. Philippe G. Ciarlet and Prof. Roderick Wong

On “Can One Hear the Shape of a Drum”

by
Professor Peter Greiner
Department of Mathematics, University of Toronto, Canada

Date: November 24, 2004 (Wednesday)
Time: 4:30 pm to 5:30 pm
Venue: Room B6605 (Faculty Conference Room)
Blue Zone, Level 6
Academic Building
City University of Hong Kong

Abstract: Mark Kac’s famous 1966 article asked the following question: “Hearing the frequencies of the sound waves produced by hitting a drum, what can one say about its shape, or geometry?” Our “drum” has the shape of an arbitrary domain in the plane with a smooth boundary, and we also allow holes in its interior. By 1966 it was known that the eigenfrequencies do yield the area of the drum and the length of its boundary. Kac was really interested in the following question: “Can one hear the number of holes, that is the Eulev characteristic, of the drum?” The answer is yes, and its true meaning, at the moment, is supplied by the Atiyah-Singer index formula, whose derivation was, and is, the main application of the calculus of elliptic pseudo-differential operators.

I shall discuss Kac’s question and its history which led to the study of the index of elliptic operators, introduce the Mikhlin-Calderon-Kohn-Nirenberg calculus of pseudo-differential operators, and connect all this with applications to scattering theory and other inverse spectral problems of physics.

(Tea, coffee and cookies will be provided at the Faculty Common Room in B6501 before the colloquium from 4:00 to 4:30 pm. Please come and join us!)

** All interested are welcome **

For enquiry: 2788-9816

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