Specialisation and Effectiveness in Number Theory (22w5024)

The Banff International Research Station will host the "Specialisation and Effectiveness in Number Theory" workshop in Banff from August 28 to September 02, 2022.

Understanding the arithmetic and geometric structure of algebraic functions is fundamental in essentially every area of mathematics and has been investigated for over a century, especially in number theory and arithmetic geometry. The workshop will focus on establishing links between functional properties of rational and algebraic functions and similar properties of their specialisations. While in one direction these links are obvious, establishing them in the opposite direction presents significant challenges. For example, understanding the arithmetic structure of points on algebraic curves has attracted a lot of attention, starting with seminal work of Faltings, Lang, Mahler, Siegel, Thue, and many others, and continuing these days to be a very active research area.

The importance of this area is especially underlined by the many crucial applications that it has to other areas such as algebraic dynamics, pseudorandomness, complex analysis, algebraic topology, quantum graphs. The present exciting and challenging problems require deep mathematical tools coming from Diophantine approximation, algebraic and analytic number theory, arithmetic geometry, and complex analysis. We will especially concentrate on new methods coming from analytic number theory, with the purpose of obtaining results of a more quantitative nature, which are rather scarce for such problems. We plan to bring together distinguished experts and younger researchers from algebraic and analytic number theory, and arithmetic geometry, to exchange ideas and develop coherent goals for future development of this exciting and active research area. This will allow us to gain a better understanding of the possibilities for further progress and attack a range of important concrete problems in this area.

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 U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).