Bi-annual Algebraic and Tropical Meetings of
Brown and YaLE

Spring 2015 @ Brown
April 30, 2015

The BATMOBYLE is a vehicle for bringing together the algebraic and tropical geometry groups of Brown and Yale for a biannual day of talks alternating between the two universities.

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).

Previous BATMOBYLEs: Fall 2014