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Texas A&M University
Mathematics

Events for 03/04/2021 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

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Time: 11:00AM - 12:00PM

Location: Zoom

Speaker: Pavel Kurasov, Stockholm

Title: Crystalline measures: from quantum graphs to stable polynomials

Abstract: Quantum graphs surprised researchers by their extraordinary spectral properties and possibility to carry out explicit analysis. One such example is given by the trace formula connecting spectra of quantum graphs to the set of periodic orbits on the underlying metric graph (without any additional correction terms). It appears that the corresponding spectral measure provides an explicit example of so-called crystalline measures generalising classical Dirac comb and Poisson summation formula.

Crystalline measures are tempered distributions given by locally finite purely atomic measures whose Fourier transform is also a purely atomic measure. Such measures were studied by J.-P. Kahane, A.-P. Guinand, and S. Mandelbrojt in the fifties. It remained unclear whether Dirac combs provide the only type of examples of crystalline measures with uniformly discrete support. We are going to show how to construct a wide family of crystalline measures using quantum graphs (differential operators on metric graphs) and more generally via stable polynomials. The measure we obtain are:

  • positive crystalline measures with uniformly discrete support;
  • Fourier quasicrystals for which every arithmetic progression meets the support in a finite set;
  • Fourier quasicrystals for which the support is a Delone set, but the support of the Fourier transform not.
Our results complement recent studies by Y. Meyer, N. Lev, A. Olevskii, and others. This is a joint work with Peter Sarnak.

Spectral Theory Reading Seminar

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Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Alberto Takase

Title:


Graduate Diversity Committee

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Time: 7:00PM - 8:00PM

Location: Zoom

Title: Diversity Reading Group Discussion: Black History Month

Abstract: Join us on Zoom as we review "Beyond Banneker: Black Mathematicians and the Paths to Excellence" by Erica N. Walker. Everyone is welcome to attend!