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BIRS Workshop — Arithmetic Aspects of Deformation Theory
15 Jan 2023 - 20 Jan 2023 • Banff, Alberta, Canada
Banff International Research Station (BIRS) for Mathematical Innovation and Discovery
One focus of modern number theory is to study symmetries of numbers that are roots of polynomial equations. Collections of such symmetries are called Galois groups, and they often encode interesting arithmetical information. The theory of Galois representations provides a way to understand these Galois groups and in particular, how they interact with other areas of mathematics. This workshop will investigate how these Galois representations can be put together into families, and search for new arithmetic applications of these families.
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Summer School — Inclusive Paths in Explicit Number Theory
02 Jul 2023 - 15 Jul 2023 • Kelowna, B.C., Canada
Banff International Research Station (BIRS) / UBCO
How primes and L-functions are linked is at the core of analytic number theory, with the Gener- alized Riemann Hypothesis (GRH) being its star conjecture. The field of explicit number theory focuses on simple yet notoriously difficult questions such as the Goldbach conjecture (Can every even number be written as the sum of two primes?) and Legendre’s conjecture (Is there a prime number between every two consecutive squares?). It is likely one of the most exacting flavors of number theory: in addition to scientific creativity, it requires precision and endurance to produce meaningful results. Working in teams with complementary expertise would allow to tackle some problems in the field more efficiently.
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Last updated: 16 November 2022