"Non UBC"@en .
"DSpace"@en .
"Kaloshin, Vadim"@en .
"2018-09-16T05:01:06Z"@* .
"2018-03-19T19:33"@en .
"M. Kac popularized the question {\em Can you hear the shape of a drum?}\nMathematically, consider a bounded planar domain $\Omega$ and the associated\nDirichlet problem $\Delta u + \lambda^2 u = 0$ with $u|_{\partial \Omega}$ = 0. The set of \n$\lambda$s such that this equation has a solution, denoted $\mathcal{L}(\Omega)$ \nis called the Laplace spectrum of $\Omega.$\nDoes Laplace spectrum determine $\Omega$? In general, the answer is negative.\n\nConsider the billiard problem inside ?. Call the length spectrum the\nclosure of the set of perimeters of all periodic orbits of the billiard. Due\nto deep properties of the wave trace function, generically, the Laplace\nspectrum determines the length spectrum. We show that any generic axis\nsymmetric planar domain with is dynamically spectrally rigid, i.e. can't be\ndeformed without changing the length spectrum. This partially answers a\nquestion of P. Sarnak. This is joint works with J. De Simoi, A. Figalli, and \nJ. De Simoi, Q. Wei."@en .
"https://circle.library.ubc.ca/rest/handle/2429/67192?expand=metadata"@en .
"45 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: University of Maryland"@en .
"Banff (Alta.)"@en .
"10.14288/1.0372059"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivatives 4.0 International"@en .
"http://creativecommons.org/licenses/by-nc-nd/4.0/"@en .
"Faculty"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Dynamical systems and ergodic theory"@en .
"Probability theory and stochastic processes"@en .
"Dynamical systems"@en .
"Can you hear the shape of a drum and deformational spectral rigidity of planar domains?"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/67192"@en .