Seminar on Number Theory and Geometry
517 Meng Wah Complex, HKU
Professor Jianya Liu
Some ideas in Number Theory
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
Arithmetic Quantum Chaos
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.
All are welcome