The question "Can one hear the shape of a drum?" was posed by Marc Kac in 1966 in an article in the American Mathematical Monthly. This question has become a central one in geometric spectral theory, a particular discipline within modern analysis, and could be solved only 30 years later by Carolyn Gordon and David Webb. In the talk the mathematics underlying this famous question will be explained together some modern aspects and developments. And not to forget, the answer will be given at the end of the talk together with a video of a short performance of a famous scientist and bongo player who lectured on the same question.
Can one hear the shape of a drum?
Wed, Oct. 6 5pm (MATH 350)
Grad Student Seminar
Chase Meadors (CU Boulder)
Some of you may know of Hilbert's famous hotel, but how do you get there from the airport? You take the transfinite subway, which has stations at every ordinal number up to the first uncountable cardinal \aleph_1, the stop at which Hilbert's hotel is located. At each station, only 1 passenger gets off the train, while a countable infinity of passengers get on. How many passengers will arrive at Hilbert's hotel? This talk will introduce basic set-theoretic concepts of ordinals and cardinals, their theory, and a key theorem that will help us get a handle on this situation, hopefully convincing you that \aleph_1 is much weirder than you may or may not have previously thought. Time permitting we will explore how this weirdness also leads to some counterexamples in other fields like topology.