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 Fridays, 5-7pm in MIT room 2-131, unless indicated otherwise below. Talks will generally run only 90 minutes, however.
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.

Spring 2017 topic: Modular representations of Gal(Qbar/Q).

References:

Deligne and Serre, Formes modulaires de poids 1, Annales scientifiques de l'ÉNS, 4e série, tome 7, no. 4 (1974), 507-530.
Ribet, A modular construction of unramified p-extensions of Q(mu_p), Inventiones Math. 34 (1976), 151-162. (See also Erickson, Ribet's converse to Herbrand's theorem for a more detailed exposition of the paper.)
Serre, Lettre à J.-F. Mestre, 13 août 1985, Contemporary Math. 67 (1987), 263-268. (For the full treatment of this topic, see Serre, Sur les représentations modulaires de degré 2 de Gal(Qbar/Q), Duke Math. J. 54 (1987), 179-230.)
Mazur and Ribet, Two-dimensional representations in the arithmetic of modular curves, Courbes modulaires et courbes de Shimura (Orsay, 1987/1988). Astérisque No. 196-197 (1991), 6, 215--255 (1992). (This provides some of the background for the next paper.)
Ribet, On modular representations of Gal(Qbar/Q) arising from modular forms, Inventiones Math. 100 (1990), 431-476.

February 10: Jun Su. Review of the analytic and algebraic aspects of modular forms, and of Galois representations (Deligne-Serre, Sections 1-3).

February 17: Vishal Arul. Representations associated to weight 1 forms: statement of the main theorem, and beginning of the proof (Deligne-Serre, Sections 4-5).

February 24: Nicholas Triantafillou. Representations associated to weight 1 forms: end of the proof, and applications (Deligne-Serre, Sections 6-9).

March 3: Alex Best. Converse to Herbrand's theorem: construction of a cusp form (Ribet 1976, Section 3)

March 10: NO SEMINAR (travel to Arizona Winter School)

March 17: Atticus Christensen. Converse to Herbrand's theorem: passing from the cusp form to a Galois representation and to the class group (Ribet 1976, Sections 4, 2, and 1)

March 24: Isabel Vogt. Serre's conjecture on 2-dimensional representations (Serre, Lettre à J.-F. Mestre)

March 31: NO SEMINAR (Spring Break)

April 7: Borys Kadets. The Picard-Lefschetz formula, and quaternions and modular curves (Ribet 1990, Section 2 and beginning of Section 3)

April 14: Lynnelle Ye. Quaternions and modular curves, continued (Ribet 1990, continuing in Section 3)

April 21: NO SEMINAR (AGNES)

April 28: Zijian Yao. Mazur's Theorem and the beginning of level changing (Ribet 1990, Section 5 and 6 and parts of 7 and 8)

May 5: Chi-Yun Hsu. End of level changing (Ribet 1990, Section 7 and 8)

May 12: Alex Smith. Bad reduction of Shimura curves (Ribet 1990, Section 4)

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. For semesters up to and including Spring 2009, see the old STAGE webpage.

Organizers: Atticus Christensen, Borys Kadets, and Bjorn Poonen (with some advice from Ben Howard and Ken Ribet)