Seminar on Topics in Arithmetic, Geometry, Etc.
STAGE is a seminar in algebraic geometry and number theory,
featuring speakers talking about work that is not their own.
Talks will be at a level suitable for graduate students.
Everyone is welcome.
Meetings are held on Wednesdays, 11-12:30pm Eastern, with a short break in the middle, in MIT room 2-449 (not online!), unless indicated otherwise below. We plan to start in September 2021, but not necessarily during the first week of classes. On September 29 and December 8, 2021, it will be 10-11:30am instead.
To receive announcements by email, add yourself to the STAGE mailing list.
If you are interested in giving one of the talks,
please contact the organizers.
Fall 2021 topic: Uniform Mordell. This is about a new uniform bound on the number of rational points on a curve of genus g at least 2, a bound that depends only on g and the Mordell-Weil rank. We may also discuss the generalization to uniform Mordell-Lang.
References to be followed:
- Gao, Recent developments of the uniform Mordell-Lang conjecture.
- Hindry and Silverman, Diophantine geometry, 2000.
- Bombieri and Gubler, Heights in Diophantine geometry, 2006.
- Lazarsfeld, Positivity in algebraic geometry I, 2004.
- Kühne, Equidistribution in families of abelian varieties and uniformity, 2021-09-05.
- Gao, Generic rank of Betti map and unlikely intersections.
- Bakker and Tsimerman, Lectures on the Ax-Schanuel conjecture.
- Gao, Ge, Kühne, The uniform Mordell-Lang conjecture, 2021-07-24.
- Szpiro, Ullmo, Zhang, Equirépartition des petits points.
- Ullmo, Positivité et discrétion des points algébriques des courbes.
- Zhang, Equidistribution of small points on abelian varieties.
Other references:
Some topics below might take more or less time than allotted.
If a speaker runs out of time on a certain date, that speaker might be
allowed to borrow some time on the next date. So the topics below might not
line up exactly with the dates below.
Past semesters: Fall 2009, Spring 2010, Fall 2010, Spring 2011, Fall 2011, Spring 2012, Fall 2012, Spring 2013, Fall 2013, Spring 2014, Fall 2014, Spring 2015, Fall 2015, Spring 2016, Fall 2016, Spring 2017, Fall 2017, Spring 2018, Fall 2018, Spring 2019, Fall 2019, Spring 2020, Fall 2020, Spring 2021
Organizers:
Tony Feng, Aashraya Jha, Hyuk Jun Kweon, Bjorn Poonen, Yujie Xu, Zhiyu Zhang