Explicit Methods in Number Theory

Abstract

The series of Oberwolfach meetings on ‘Explicit methods in number theory’ brings together people attacking key problems in number theory via techniques involving concrete or computable descriptions. Here, number theory is interpreted broadly, including algebraic and analytic number theory, Galois theory and inverse Galois problems, arithmetic of curves and higherdimensional varieties, zeta and $L$-functions and their special values, modular forms and functions. The 2021 meeting featured a seven-lecture minicourse on the distribution of class groups and Selmer groups. The other talks covered a broad range of topics in number theory ranging, for instance, from deterministic integer factorisation to the inverse Galois problem, rational points, and integrality of instanton numbers.