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 Thursdays, 4pm-5:30pm, with a short break in the middle, in MIT room 2-131 (not online!), unless indicated otherwise below.
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 2023 topic: Mazur's theorem on torsion of elliptic curves over Q.

Prerequisites: Algebraic geometry, number theory, basic arithmetic theory of elliptic curves, basic analytic theory of modular forms as in Serre, A course in arithmetic.

Main references:

[Ma1] Mazur, Modular curves and the Eisenstein ideal
[Ma2] Mazur, Rational isogenies of prime degree
[MT] Mazur and Tate, Points of order 13 on elliptic curves

References:

[BLR] Bosch, Lutkebohmert, and Raynaud, Néron Models
[DR] Deligne and Rapoport, Les Schémas de Modules de Courbes Elliptiques (in Modular Functions of one Variable II edited by Deligne and Kuijk)
[DS] Diamond and Shurman, A First Course in Modular Forms
[KM] Katz and Mazur, Arithmetic Moduli of Elliptic Curves
[Mi1] Milne, Abelian varieties
[Mi2] Milne, Jacobian varieties (in Arithmetic Geometry edited by Cornell and Silverman)
[Mu] Mumford, Abelian Varieties
[Si1] Silverman, The Arithmetic of Elliptic Curves
[Si2] Silverman, Advanced Topics in the Arithmetic of Elliptic Curves
[Ta] Tate, Finite flat group schemes (in Modular forms and Fermat's Last Theorem edited by Cornell, Silverman, and Stevens)

Miscellaneous:

Andrew Snowden taught a course on this at the University of Michigan in 2013. His notes and lectures are an excellent resource (especially for speakers).
Tom Weston has some notes providing a relatively non-technical introduction to the special case of 11-torsion and the modular curves of level 11.
Notes from a seminar run at Stanford some years ago on a very similar topic (focusing more on [Ma2] above).

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, Fall 2021, Spring 2022, Fall 2022, Spring 2023

Organizers: Niven Achenjang, Edgar Costa, Zhao Yu Ma, Bjorn Poonen, Vijay Srinivasan.