BARD 2 Schedule

A live oak draped in Spanish moss in City Park, New Orleans. Photo by Olivia Beckwith.

BARD 2 will take place at Tulane in New Orleans during the afternoon of April 18, 2022, with a pre-talk taking place over Zoom the previous Friday. See the schedule below. Talks will take place in the Lavin-Bernick Center for University Life in room 203 (Stibbs Conference Room); all times are US Central Time.

A visitor parking pass can be purchased using this link. The pass should be used at the Diboll Parking Garage.

3:00pm–4:30pm, Friday, April 14: Pre-talk by Michael Allen and Olivia Beckwith. (Zoom)

12:00pm–12:45pm, Tuesday, April 18: Lavin-Bernick Center Room 203 for registration and sandwiches.

12:45pm–1:45pm: Plenary lecture by Jesse Thorner.

A new approach to zero-free regions of L-functions

I will present a new approach to establishing zero-free regions of L-functions. The approach is applicable to Rankin-Selberg L-functions for which the method of de la Vallee Poussin is not yet known to be applicable. Applications include the strongest known error term in the prime number theorem for all Rankin-Selberg L-functions. This is joint work with Gergely Harcos.

1:45pm–2:00pm: Coffee and snacks.

2:00pm–3:00pm: Plenary lecture by Kim Klinger-Logan.

A shifted convolution problem arising from physics

Physicists Green, Russo, and Vanhove have discovered solution to differential equations involving automorphic forms appear at the coefficients to the 4-graviton scattering amplitude in type IIB string theory. Specifically, for $\Delta$ the Laplace-Beltrami operator and $E_s(g)$ a Langlands Eisenstein series, solutions $f(g)$ of $(\Delta-\lambda)f(g) = E_a(g) E_b(g)$ for $a$ and $b$ half-integers on certain moduli spaces $G(Z){\backslash}G(R)/K(R)$ of real Lie groups appear as coefficients to the analytic expansion of the scattering amplitude. We will briefly discuss different approaches to finding solutions to such equations and focus on a shifted convolution sum of divisor functions which appears as the Fourier modes associated to the homogeneous part of the solution. Initially, it was thought that, when summing over all Fourier modes, the homogeneous solution would vanish but recently we have found an exciting error term. This is joint work with Stephen D. Miller, Danylo Radchenko and Ksenia Fedosova.