Fall quarter at UW begins!

All good things must come to an end! It's been a gloriously warm and sunny summer, but with the advent of august this week the rain is due to set in. Cue the six months in Seattle where you don't see the sun (I've started taking my vitamin D supplements again).

This week also sees the University of Washington start back up again: Wednesday 24 September is the first day of fall quarter classes. I will be teaching two sections of MATH307: Introduction to Differential Equations. My website for the course is up and running at http://www.math.washington.edu/~mlungu/teaching/math307au14/index.html - go take a look (and let me know if there are any typos)!

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.

Bristol

This week finds me in Bristol, in southwest England. I'm here for a weeklong summer school officially titled the Building Bridges: 2nd EU/US Summer School on Automorphic Forms and Related Topics (catchy title!). The summer school comprises of three mini-courses run by pairs of mathematicians in the area of mathematics that I'm in; it's also being co-organized by of of the mentors of my Google Summer of Code project, who is resident here in England. Thus attending will be a great way to kill multiple birds with one stone: learn some new and cool math, see a new place, and get to chat to people relating to my GSoC project as well.

As such, posts on analytic rank estimation of elliptic curves and $L$-functions might be a bit thin on the ground this week. I'll try do a little bit when I can, but they're keeping us fairly busy here.

Bristol, from what I've seen of it so far, is quite beautiful. The sun has been shining this week (which always helps), but the part of town that I'm staying in - the recently revitalized Docklands area - is clean, picturesque, and buzzing with activity. The city has pushed for sustainability and pedestrian-friendliness in recent years, and it shows.

All in all, can't complain. I think it will be a wonderful week.

Two Weeks Down South

Back from South Africa!

I've just spent a fortnight back in my motherland. I went over for a number of reasons: first and foremost, my US F-1 visa was due to expire soon, so I needed to renew it in order to continue to be able to enter and exit the country while I'm still studying here. While in SA I also voted (the South African national elections were held on May 5) and renewed my pilot's license.

Consequently, very little math or coding has occurred in the past two weeks. So: time to get back in the swing of things! Stay tuned folks.

- Simon