In February of 2010 I gave a 12-hour course at the CRM in Barcelona on “Curves and Jacobians over function fields.” This was more advanced than Park City in that I discussed curves of higher genus and function fields over arbitrary (as opposed to finite) fields. The notes are under review and comments would be most welcome.
Two recent papers:
- In Arithmetic of Jacobians in Artin-Schreier extensions, Rachel Pries and I study Artin-Schreier analogues of results proven in the Kummer tower in my article 2007b, Lisa Berger's thesis, and 2013a.
- In Explicit points on the Legendre curve II, Ricardo Conceição, Chris Hall and I study points on the Legendre curve over extensions Fq(t1/d) of Fp(t) and show that there are points of infinite order for many values of d. One might expect that there are such points only when d divides pf+1 for some f, but it turns out that there are many more interesting values of d.
I have projects for students at several levels. Here is an undergraduate research project (which is not as scary as it might seem at first ...). I'd be happy to talk with graduate students about projects in number theory and algebraic geometry ranging from a quick MS with good prospects for a paper to more substantial PhD projects.
My current office hours are Mondays 2:00 - 3:00 and Tuesdays 3:00 - 4:00. Setting up an appointment by e-mail is the best way to see me. My assistant Sharon McDowell also has my schedule.
My medium length CV.
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