L-functions, zeta-functions and lattices in large dimension

Research Project, 2022 – 2025

The proposed research program consists of a detailed investigation of several fundamental problems in analytic number theory and related research areas. Our focus will be on open problems related to zeros of L-functions and the value distribution of zeta functions connected to the geometry of numbers, as well as deep questions from the intersection of analytic number theory and arithmetic statistics.
We expect that the proposed research will require a wide range of techniques from number theory, algebra, analysis and geometry.The research will be carried out during 2022-2025 by the project leader in collaboration with national and international colleagues. This is a project in basic science and it is hard to give a precise time plan; in particular since several parts of the project are expected to require significant time to be completed.The proposed research program will lead to the development of new tools and techniques, as well as a general progression of our understanding of central questions, in analytic number theory, the geometry of numbers and arithmetic statistics. In particular, we expect to develop new techniques in an emerging area at the intersection of analytic number theory and arithmetic statistics in order to address the non-vanishing problem in geometric families. Another main goal is to develop tools that make it possible to attack outstanding and currently intractable problems in the geometry of numbers including the lattice sphere packing problem.