Date:
Thu, 03/07/202512:01-13:55
Location:
Ross 70
Title: On the spectrum of the clamped round plate.
Abstract: Siegel has shown in 1929 that all multiplicities in the spectrum of an elastic round membrane are due to its rotational symmetry, i.e. every eigenfunction is of a separated form. We give some background on his solution and then we discuss the case of a clamped round plate. Is every eigenfunction of the clamped round plate of a separated form?
We prove that any eigenfunction is a linear combination of at most two separated ones, and we relate this problem to Schanuel's conjecture from Transcendental Number Theory. The talk is based on joint work with Dan Mangoubi.
Abstract: Siegel has shown in 1929 that all multiplicities in the spectrum of an elastic round membrane are due to its rotational symmetry, i.e. every eigenfunction is of a separated form. We give some background on his solution and then we discuss the case of a clamped round plate. Is every eigenfunction of the clamped round plate of a separated form?
We prove that any eigenfunction is a linear combination of at most two separated ones, and we relate this problem to Schanuel's conjecture from Transcendental Number Theory. The talk is based on joint work with Dan Mangoubi.