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Douglas Ulmer
Professor and Chair |
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News
The School of Mathematics recently hosted an event for a small group of alumni and friends to discuss ways that they might get involved with the School. Here are pdf slides of presentations giving an overview of the School by me, outreach programs by Maria Westdickenberg, undergraduate research by Matt Baker, interdisciplinary programs by Prasad Tetali, and the graduate student experience by Mitch Keller.
Older news is here
Research
Two recent papers:
- On Mordell-Weil groups of Jacobians over function fields reconsiders the construction in Lisa Berger's thesis (Arizona, 2007, published in the Journal of Number Theory) and uses it to give an interesting formula for ranks of Jacobians of certain curves over k(t) where k is any perfect field.
- Explicit points on the Legendre curve gives a remarkably elementary construction of an elliptic curve over Fp(t) with explicit points generating a group of arbitrarily large rank. There appear to be many interesting related questions and generalizations.
My medium length CV.
Lectures
Slides from a conference in honor of Dick Gross.
I gave a 5-lecture course at the Park City Math Institute in summer 2009 on “Elliptic curves over function fields.” Here are the slides:
For a version more suitable for printing, add -doubled, e.g., Lecture1-doubled.pdf.
I'll be giving a 12-hour course about similar questions for higher genus curves at the CRM in Barcelona in late February.
Students
Office hours: Generally Tuesdays 2:00 - 4:00 and Thursdays 2:00 - 3:00. It's a good idea to e-mail first to make sure there are no changes this week.
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.
| email: ulmer@math.gatech.edu | phone: 404-894-2747 | office: Skiles 118B |