Generalized Gauss maps and Farey statistics (12frg172)


(University of Washington)

Jonathan Chaika (University of Chicago)

Yitwah Cheung (Tsinghua University)

(Université Paris-Sud)

(University of Victoria)


The "Generalized Gauss maps and Farey statistics" workshop will be hosted at The Banff International Research Station.

Many important problems in Number Theory concern with distribution of various randomly occurring numbers, e.g. the Riemann Hypothesis is concerned with the distribution of prime numbers. Sometimes the randomness can be explained by means of a classical dynamical system, in which case the powerful tools of ergodic theory can be brought to bear. However, it is very difficult to predict when this will happen in general. This FRG will look at Farey sequences, whose relation to horocycle flows have recently been discovered, and seeks to improve the range of random phenomena that can be understood in terms of classical dynamical systems.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí255a (CONACYT).