Nelson's work has resulted in the first convexity-breaking bounds for a large class of L-functions on the critical line (including all the standard ones of GL(n)). This marks a significant advance in a field initiated one hundred years ago by Hermann Weyl in the context of the Riemann Zeta function. Nelson analyzes L-values via certain associated automorphic periods. His effective strategy comprises several elements, including refining the orbit method developed in prior work with Venkatesh, and analyzing the geometric aspect of a relevant Relative Trace Formula, enabling the application of Amplification.

"I'm glad to hear that I received this prize. It's a great honor. I hope it brings further attention to some of the interesting open problems in the field.”

– Paul Nelson

The Clay Research Awards celebrate the outstanding achievements of the world’s most gifted mathematicians. The venue where The Clay Research Awards are being presented is the Clay Research Conference and Workshops. Read more here:

• https://www.claymath.org/clay-research-award/