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Workshops & seminars

Mathematics & Statistics visitor seminar

Quantum Chaos and Arithmetic


Date & time
Tuesday, January 24, 2017
1:30 p.m. – 3 p.m.
Cost

This event is free

Contact

Ms. Geraldine Ford
3232

Where

J.W. McConnell Building
1400 De Maisonneuve W.
Room 921-4

Wheel chair accessible

Yes

SPEAKER: Dr. Stephen Lester

(Concordia University & CRM-ISM)

ABSTRACT:  In this talk I will discuss some problems in Quantum Chaos and describe results in arithmetic settings where more can be proved. Given a compact, smooth Riemannian manifold (M,g) a central problem in Quantum Chaos is to understand the behavior of eigenfunctions of the Laplace-Beltrami operator in the limit as the eigenvalue tends to infinity.  The Quantum Ergodicity Theorem of Shnirelman, Colin de Vediere, and Zelditch asserts that if the geodesic flow on M is ergodic then the  mass of almost all of the eigenfunctions equidistributes.  I will discuss problems which go beyond the Quantum Ergodicity Theorem such as quantum unique ergodicity and small scale quantum ergodicity in the setting of arithmetic surfaces such as the torus and modular surface.  Limitations on equidistribution will also be discussed.  I will also indicate how these problems are related to arithmetic objects such as L-functions, modular forms, and multiplicative functions.

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