Conference: Recent Perspectives on Moments of L-functions

This award provides support for the conference “Recent Perspectives on Moments of L-functions,” which will be held at the University of Texas at Dallas from June 1-2, 2026. The concept of an L-function is a mathematical object in the field of Number Theory used to study arithmetic data such as the prime numbers. The conference will focus on the broad theme of understanding L-functions through statistical information known as “moments.” The conference will bring together experts in the field to present recent advances, and other researchers in the area, to exchange ideas and build collaborations. Most of the participants will be early-career researchers--graduate students, postdoctoral researchers, and assistant professors--who will benefit from the conference’s stimulating environment. The study of moments of L-functions, both on the critical line and in families at the central point, has been a fruitful and robust way to understand L-functions and obtain a myriad of applications, including subconvexity bounds and non-vanishing results. This conference will showcase various distinct approaches to moments of L-functions that have been remarkably successful in recent times. Some of these approaches include reciprocity formulae for moments of L-functions, the delta symbol method, higher rank trace formulae and families, and asymptotics for moments of L-functions over special families. The conference will encourage researchers working with one approach to learn about other approaches, with the goals of establishing new links between the different techniques and the development of novel methods. More information on the conference can be found at https://sites.google.com/view/l-functions-utd/home. 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.