Seminar on Number Theory and Geometry
517 Meng Wah Complex, HKU
Professor Jianya Liu
Some ideas in Number Theory
Abstract
In
this talk, I will try to explain some important ideas in Number Theory from a
historical and philosophical perspective, so that they are accessible to
general audiences. In particular, I will explain the following in a very crude
way:
(1) The
idea of Riemann to connect arithmetic problems with distribution of zeros of L-functions;
(2) The
idea of Dirichlet, Birch and Swinnerton-Dyer
to link arithmetic/geometric problems with special values of L-functions;
(3) The
idea of Shimura and Taniyama to link arithmetic/geometric
L-functions with automorphic
L-functions;
(4) The
Langlands program and
structure of automorphic L-functions.
4:00
– 4:20pm Tea
Break
Dr. Yuk-Kam
Lau
The
Arithmetic
Quantum Chaos
Abstract
Quantum
mechanics and classical mechanics have fundamental differences, for instance, a
point particle is described by a probability density rather than by a
trajectory as in classical mechanics.
The study of Quantum chaos is
concerned with the characterization of the properties of quantum systems in
relation to their underlying classical dynamical systems. Arithmetic quantum chaos refers to the investigation of quantum
systems equipped with arithmetic structures. These additional structures allow
extensive analysis with tools and techniques in Number Theory.
In this
talk, we shall give an expository introduction to some aspects of arithmetic
quantum chaos. No prior knowledge of classical or quantum mechanics is assumed.
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All are welcome |
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