Conference: The Gross-Zagier Formula, 40 Years Later

This award provides participant support for the conference “The Gross–Zagier Formula, 40 Years Later,” which will take place at the Massachusetts Institute of Technology from August 3-7, 2026. The Gross–Zagier formula is a fundamental result in the mathematical field of number theory relating a special solution of a certain degree-three Diophantine equation to the vanishing of a special function called an L-function. This result has provided some of the strongest evidence to date for the conjecture of Birch and Swinnerton-Dyer for elliptic curves, one of the seven Millennium Prize Problems. The conference will feature lectures by experts covering a broad range of recent advances connected with the Gross–Zagier formula, its generalizations, and the work it has inspired. Most participants will be early-career researchers who will benefit from the conference’s stimulating environment and fresh perspectives.

New directions have recently emerged surrounding fundamental questions connecting special values and derivatives of automorphic L-functions with algebraic cycles, the method of Euler systems, and period integrals of automorphic forms. This has inspired applications to generalizations of the Birch and Swinnerton-Dyer conjecture for higher-dimensional algebraic varieties. The conference will showcase an array of advances, including those related to Kudla’s program, the Gan–Gross–Prasad conjecture, and the relative Langlands program. Some lectures will be survey talks outlining different branches of current research related to the Gross–Zagier formula, with the aim of introducing the main themes to early-career participants. More information about the conference can be found at https://math.mit.edu/events/gross-zagier/.

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.

Award Number: 2603742
Principal Investigator: Wei Zhang
Funds Obligated: $49,000
State: MA