Colóquio - CAN ONE COUNT THE SHAPE OF A DRUM?

Data de Início: 
quinta-feira, 26 Março, 2015 - 16:00
Palestrante: 
Dr. Uzy Smilansky - Weizmann Institute - Israel
Local: 
Auditório Abrahão de Moraes

Several decades ago Mark Kac asked his famous question:"Can one hear the  shape of the drum?" - in other words- under which  conditions, if at all, can the frequency spectrum of the drum  vibrations determine the shape of the drum's boundary.This problem has many important implications in physics and  mathematics, and in the  first part of the talk I shall review the present status of this  subject. In the second part, I shall address the new version of the  question,  in which one replaces "hear" by "count". That is, instead  of considering the sequence of frequencies, one considers the  sequence  of the nodal numbers (the number of domains where the wave-function  has the same sign) of the corresponding wave functions. I'll show that  this sequence of integers stores information on the shape of the drum.  Moreover, counting the drum in this way can also resolve ambiguous  drums which have different shapes but produce the same spectra of vibrations.

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Desenvolvido por IFUSP