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, 3-5pm 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 2019 topic: Unlikely intersections and o-minimality.

References to be followed:

Scanlon, O-minimality as an approach to the André-Oort conjecture, Around the Zilber-Pink conjecture/Autour de la conjecture de Zilber-Pink, 111-165, Panor. Synthèses, 52, Soc. Math. France, Paris, 2017.
Lang, Algebraic number theory, second edition, Springer, 1994, Chapter XVI on the Brauer-Siegel theorem.
Tsimerman, The André-Oort conjecture for A_g, Ann. of Math. (2) 187 (2018), no. 2, 379-390. (The link works only at MIT.)
Bakker, Klingler and Tsimerman; Tame topology of arithmetic quotients and algebraicity of Hodge loci, arXiv:1810.04801.

Other references:

Pila, O-minimality and Diophantine geometry, Proceedings of the International Congress of Mathematicians-Seoul 2014. Vol. 1, 547-572, Kyung Moon Sa, Seoul, 2014.
Scanlon, Counting special points: logic, Diophantine geometry and transcendence theory, Bull. Amer. Math. Soc. (N.S.) 49 (2012), no. 1, 51-71.
Marker, Model theory: an introduction, Graduate Texts in Mathematics, 217. Springer-Verlag, New York, 2002.
Pila and Wilkie, The rational points of a definable set, Duke Math. J. 133 (2006), no. 3, 591-616.
Pila and Tsimerman, Ax-Lindemann for A_g, Ann. of Math. (2) 179 (2014), no. 2, 659-681. (The link works only at MIT.)

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.

February 8: Vishal Arul. Overview of the Pila-Wilkie strategy (Scanlon, O-minimality, Sections 1 and 2)

February 15: Yibo Ji. Review of first-order logic, and o-minimality (Scanlon, O-minimality, Section 3)

February 22: Borys Kadets. The Pila-Wilkie counting theorem

March 1: NO MEETING (eve of Arizona Winter School)

March 8: Atticus Christensen. Proof of the Manin-Mumford conjecture using o-minimality.

March 15: Yongyi Chen. Pila's André-Oort theorem.

March 22: NO MEETING (eve of Spring Break)

March 29: NO MEETING (Spring Break)

April 5: Junho Peter Whang. Andre-Oort for A_g (meeting 10am-noon in 2-255)

April 12: Alex Best. The Brauer-Siegel Theorem

April 19: NO MEETING

April 26: Junho Peter Whang (meeting 10am-noon in 2-255).

May 3: NO MEETING

May 10: NO MEETING

May 17: Nicholas Triantafillou.

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

Organizers: Atticus Christensen, Bjorn Poonen, Yichi Zhang.