Can you hear the shape of a drum? and deformational spectral rigidity
2023-05-23 15:00:00
2023-05-23 15:00:00
2023-05-23 15:00:00
Speaker : 3:00PM, Vadim Kaloshin
Time : 2023-05-23 15:00:00
Location : May
Title: Can you hear the shape of a drum? and deformational spectral rigidity
Speaker: Vadim Kaloshin (Austrian Institute of Science and Technology)
Time: Tuesday, May 23, 2023, 15:00-18:00
Location: Zoom 915 4821 3645, Password 202305
Abstract: M. Kacpopularized the following question Can one hear the shape of a drum? Mathematically, consider a bounded planar domain Ω ⊆ R2 with a smooth boundary and the associated Dirichlet problem Δu + λu = 0, u|∂Ω=0. The set of λ's for which this equation has a solution is called the Laplace spectrum of Ω. Does the Laplace spectrum determine Ω up to isometry? Consider the billiard problem inside Ω. Call the length spectrum the closure of the set of perimeters of all periodic Due to deep properties of the wave trace function, generically, the Laplace spectrum determines the length spectrum. Jointly with J. De Simoi and Q. Wei, we show that an axially symmetric domain close to the circle is dynamically spectrally rigid, i.e. cannot be deformed This partially answers a question of P. Sarnak.