|
Joe Rabinoff (Georgia Tech) |
Uniformity of rational points and tropical geometry
A recent result of Stoll uses p-adic integration to prove that there is a number N(g) such that for all hyperelliptic curves X/Q of genus g ≥ 2 and Mordell--Weil rank r ≤ g-3, one has #X(Q) ≤ N(g). This is a special case of the uniform Mordell conjecture. I'll show how linear systems on metric graphs can be employed to extend Stoll's theorem to all curves X/Q with r ≤ g-3. I'll also indicate how these techniques along with more refined structure theory of Berkovich curves can be used to prove special cases of the uniform Manin--Mumford conjecture. This work is joint with Eric Katz and David Zureick--Brown. |
| 11:00 - 12:00 | Morning Talk: TBA Nathan Kaplan (Yale) |
CIT 269 |
| 12:00 - 02:00 | Lunch | |
| 02:00 - 03:00 | Afternoon Talk: TBA Jennifer Park (McGill) |
CIT 269 |
| 03:00 - 04:00 | Tea | Common room |
| 04:00 - 05:00 | Plenary Talk: Uniformity of rational points and tropical geometry Joe Rabinoff (Georgia Tech) |
CIT 269 |
Brown Organizers:
Dan Abramovich (Brown),
Melody Chan
(Harvard), and
Nathan Pflueger (Brown).
Yale Organizers:
Asher Auel (Yale),
Angie Cueto (Columbia),
José González (Yale),
Nathan
Kaplan (Yale), and
Sam Payne (Yale).