Bristol Summer School Recap

For the past week I've been in Bristol, England, attending a summer school on computing with L-functions and automorphic forms. The official name of the summer school was the Building Bridges Summer School on Automorphic Forms and Related Topics.

The school comprised of three intense 2-day long mini-courses, each hosted by a pair of mathematicians in the field:

• Explicit Methods for Modular Forms and $L$-functions by Tim Dokchitser and John Cremona, on various methods for computing with modular forms, elliptic curves and $L$-functions;
• The Legacy of Ramanujan by Bill Duke and Paul Jenkins, on singular moduli, Borcherds products and forms of half-integral weight;
• The Langlands Program by Solomon Friedberg and Jim Codell, on the web of conjectures relating automorphic forms, automorphic representations and $L$-functions.

The reason I attended the summer school is that the subjects all tie directly to the work that I am currently doing - both for my Google Summer of Code project and work towards my dissertation. The central objects of all three mini-courses are motivic $L$-functions - of which elliptic curve $L$-functions are an example. It would take me quite a long time to go through all the math we covered at the summer school - over the course of last week I took 114 pages of lecture notes! This is unfeasible - if you're interested please follow the links above, at which you should find typed up notes of all of the lectures.

Instead, my next post will focus on one of the aspects that ties in with both my GSoC project and my dissertation work: The full Birch and Swinnerton-Dyer conjecture, and how we can use it to obtain results about the complexity of computing analytic rank.