SMS scnews item created by Zhou Zhang at Thu 4 Aug 2011 1021
Type: Seminar
Modified: Mon 8 Aug 2011 1321; Wed 10 Aug 2011 1139
Distribution: World
Expiry: 1 Sep 2011
Calendar1: 26 Aug 2011 1430-1530
CalLoc1: Carslaw 175
Auth: zhangou@bari.maths.usyd.edu.au

# Public Lecture and Colloquium: Sarnak -- Topics in Number Theory

There is a poster (~2MB) at

http://www.maths.usyd.edu.au/u/zhangou/Sarnak.pdf

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The Mahler Lectures are a biennial activity organised by the Australian Mathematical
Society with the assistance of the Australian Mathematical Sciences Institute.
Initiated by a bequest from number theorist Kurt Mahler, it brings a renowned
mathematician to Australia to give a lecture tour (including public lectures) of
Australian universities.

This year’s Mahler Lecturer is Peter Sarnak, Eugene Higgins Professor of Mathematics at
Princeton University and Professor at the the Institute for Advanced Study in
Princeton.  He is a legendary figure in modern number theory. Peter Sarnak will be in
Australia from August 8 till August 27 and will give 13 lectures at 9 different
universities in 6 different cities. His lecture on August 12 will be an AGR lecture and
will therefore be accessible to the mathematical community right across Australia.

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Thursday, Aug. 25, UNSW, Clancy Auditorium, 3.30pm, Public Lecture

Chaos, Quantum Mechanics and Number Theory

The correspondence principle in quantum mechanics is concerned with the relation between
a mechanical system and its quantization.  When the mechanical system is relatively
orderly ("integrable"), then this relation is well understood.  However when the system
is chaotic much less is understood.  The key features already appear and are well
illustrated in the simplest systems which we will review.  For chaotic systems defined
number-theoretically, much more is understood and the basic problems are connected with
central questions in number theory.

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Friday, Aug. 26, Sydney University, 2.30pm, Room 175, Carslaw Building, Colloquium

Zeroes and Nodal Lines of Modular Forms

One of the consequences of the recent proof by Holowinski and Soundararajan of the
holomorphic "Quantum Unique Ergodicity Conjecture" is that the zeros of a classical
holomorphic hecke cusp forms become equidistributed as the weight of the form goes to
infinity.  We review this as well as some finer features (first discovered numerically)
concerning the locations of the zeros as well as of the nodal lines of the analogous
Maass forms.  The latter behave like ovals of random real projective plane curves, a
topic of independent interest.


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