BARD 4 Schedule

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

BARD 4 will take place at Tulane University in New Orleans during the afternoon of October 18, 2024, with a pre-talk taking place over Zoom the previous Friday. See the (tentative) schedule below. Talks will be held in Richardson Building room 115; all times are US Central Time. Talks will also be streamed on Zoom at https://tulane.zoom.us/j/94674171828.

3:30pm–4:30pm, Friday, October 11: Pre-talk by Edna Jones (on Zoom)

12:00pm–12:45pm, Friday, October 18: Registration and light lunch (Richardson Building 115)

12:45pm–1:45pm: Plenary lecture by Ayla Gafni (Richardson Building 115)

Exponential sums twisted by additive functions

For an arithmetic function $f$ and a real number $\alpha$ , consider the exponential sums $S_f(x,\alpha) = \sum_{n\le x} f(n) e^{2\pi i n \alpha}.$ The growth of these sums as $x$ increases plays an important role in many number theory techniques. We will discuss new bounds on these exponential sums for various additive functions $f$ , including $\omega(n)$ (the number of distinct prime factors of $n$ ) and $\Omega(n)$ (the total number of prime factors of $n$ ). We will then apply these bounds to enumerate certain integer partitions and solutions to Diophantine equations. This is joint work with Nicolas Robles.

1:45pm–2:00pm: Break

2:00pm–3:00pm: Plenary lecture by Joshua Males (Richardson Building 115)

Oscillating asymptotics of partition classes, central L-values, and open questions

In this talk I’ll give a quick overview of two recent papers. The first will be on oscillating asymptotics for coefficients of a Nahm-type sum, settling a 40-year old conjecture of Andrews, and obtaining the first glimpse of links of a hypergeometric series to the arithmetic of an imaginary quadratic field. The second focus will be on determining the (non-)vanishing of central L-values of newforms, their relationship to so-called locally harmonic Maass forms, and older observations of Zagier.

3:00pm–3:30pm: Coffee and snacks (Richardson Building 115)

3:30pm–5:00pm: Lightning talks (Richardson Building 115)

6:00pm: Dinner at Joey K’s