BARD 5 Schedule

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

BARD 5 will take place at Xavier University of Louisiana in New Orleans during the afternoon of March 27, 2025, with a pre-talk taking place over Zoom the previous Friday. See the schedule below. Talks will be held on the Xavier campus in the Norman C. Francis Annex Building (NCF; click to see map); all times are US Central Time. See Resources for transportation and parking information. Talks will also be streamed on Zoom.

3:30pm–4:30pm, Friday, March 21: Pre-talk by Lucas Villagra Torcomian (on Zoom)

12:00pm–12:45pm, Thursday, March 27: Registration and light lunch (NCF-568)

12:45pm–1:45pm: Plenary lecture by Ling Long (NCF-568; Zoom link)

Hypergeometric Functions and Modular Forms

Hypergeometric functions are special functions playing important roles in mathematics and physics. The theories of hypergeometric functions and modular forms are highly intertwined. In this talk, we will give an overview of the theories leading to an explicit “Hypergeometric-Modularity” method for associating a modular form to a given hypergeometric datum. It is based on joint papers with Michael Allen, Brian Grove and Fang-Ting Tu, as well as a more recent paper by Esme Rosen.

1:45pm–2:00pm: Break

2:00pm–3:00pm: Plenary lecture by Michael Bennett (NCF-568; Zoom link)

The Ramanujan-Nagell equation, yet again!

In this talk I discuss various approaches to bounding the number of solutions to the Diophantine equation

$x^2+D=p^\alpha q^\beta$

where $p$ and $q$ are prime. Previous work of Evertse and of Yamada have relied upon hypergeometric functions and Pade approximation, while our new work uses instead bounds for linear forms in logarithms to obtain sharper bounds.

3:00pm–3:30pm: Coffee and snacks (NCF-568)

3:30pm–5:00pm: Lightning talks (NCF-568; Zoom link)

6:00pm: Dinner at TBA