Conference: International Conference on L-functions and Automorphic Forms

Vanderbilt University, Nashville TN

Investigators

Abstract

This award provides support for the conference entitled "International Conference on L-functions and Automorphic Forms'', which will take place at Vanderbilt University in Nashville, Tennessee on May 13--16 2024. This is part of an annual series hosted by Vanderbilt, known as the Shanks conference series. The main theme will be on new developments and recent interactions between the areas indicated in the title. The interplay between automorphic forms and L-functions has a long and very fruitful history in number theory, and bridging both fields is still a very active area of research. This conference is oriented at establishing and furthering dialogue on new developments at the boundary of these areas. This will foster collaboration between researchers working in these fields. One beautiful feature of modern number theory is that many problems of broad interest, in areas of study as diverse as arithmetic geometry to mathematical physics, can be solved in an essentially optimal way if the natural extension of the Riemann hypothesis holds for L-functions associated to automorphic representations. Although many generalizations and applications around L-functions have have already been worked out, there are still various fundamental open problems among them to tackle, including bounds for and the value distribution of L-functions. The former is related to the pursuit of so-called sub-convexity bounds for L-functions. The latter is related to the Birch and Swinnterton-Dyer conjecture (another “Millenium problem” posed by the Clay Mathematics institute). These pursuits are closely connected with the Langlands program, a “grand unifying theory” relating automorphic forms. Further details can be found on the conference website https://my.vanderbilt.edu/shanksseries/. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.