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 2-132, 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.

Fall 2016 topic: Tropical geometry.

References:

Payne, Topology of nonarchimedean analytic spaces and relations to complex algebraic geometry, Bulletin of the AMS 52 (2015), 223-247. (An optional additional introduction - see Sections 1-3.)
Gubler, A guide to tropicalizations, pp. 125-189 in: Algebraic and combinatorial aspects of tropical geometry, AMS, 2013. (We will do only Sections 1-5.)
Baker, Payne, and Rabinoff, On the structure of non-archimedean analytic curves, pp. 93-121 in: Tropical and Non-Archimedean Geometry, AMS, 2013.
Seminar on tropical Brill-Noether theory, Spring 2016. (Probably we will do only Lecture 8.)
Baker and Faber, Metric properties of the tropical Abel-Jacobi map, J. Alg. Combinatorics 33 (2011), 349-381. (We need mainly Theorem 4.1.)
Mikhalkin and Zharkov, Tropical curves, their Jacobians and theta functions, pp. 203-230 in: Curves and abelian varieties, AMS, 2008.
Baker and Rabinoff, The skeleton of the Jacobian, the Jacobian of the skeleton, and lifting meromorphic functions from tropical to algebraic curves, IMRN 15 (2015), 7436-7472.
McCallum and Poonen, The method of Chabauty and Coleman, 99--117 in: Explicit methods in number theory; rational points and diophantine equations, Panoramas et Synthèses 36, Société Math. de France, 2012.
Katz, Rabinoff, Zureick-Brown, Diophantine and tropical geometry, and uniformity of rational points on curves (a survey covering the paper below, and many other topics).
Katz, Rabinoff, Zureick-Brown, Uniform bounds for the number of rational points on curves of small Mordell-Weil rank, to appear in Duke Math. J. This generalizes the breakthrough by Michael Stoll for hyperelliptic curves to arbitrary curves.

September 9: Yuzhou Gu. Berkovich analytification, tropicalization, models over DVRs, initial degeneration (Gubler, Sections 2-5)

September 16: Changho Han. Skeleton of an annulus, semistable decompositions and skeleta of curves (Baker-Payne-Rabinoff, Sections 2 and 3)

September 23: NO SEMINAR (Student holiday)

September 30: Dennis Tseng. Semistable models and the Poincaré-Lelong formula (Baker-Payne-Rabinoff, Section 4)

October 7: NO SEMINAR (Building 2 dedication and retreat)

October 14: Soohyun Park. Metric structure on an analytic curve (Baker-Payne-Rabinoff, Section 5), divisor theory on metric graphs (Lecture 8 of the Seminar on tropical Brill-Noether theory)

October 21: Mitchell Lee. Jacobians of metric graphs (Baker-Faber Theorem 4.1; see also Mikhalkin-Zharkov)

October 28 at 5:30pm: Nicholas Triantafillou. Skeleton of the Jacobian: overview and uniformization (Baker-Rabinoff, Sections 1-4, but most of Section 3 was covered in more detail in the previous week)

November 4: NO SEMINAR (AGNES)

Thursday November 10, 5-7pm in 2-139: Geoffrey Smith. Skeleton of the Jacobian: retraction of divisors and divisor classes, end of proof (Baker-Rabinoff, Sections 5 and 6)

November 11: NO SEMINAR (Veterans Day)

Thursday November 17, 5-7pm in 2-135: Chi-Yun Hsu. p-adic integration (McCallum-Poonen, and Section 3 of the Katz, Rabinoff, Zureick-Brown paper in Duke)

November 25: NO SEMINAR (Thanksgiving Break)

December 2: Alex Smith. Uniform bounds for the number of rational points on curves of small Mordell-Weil rank (Katz, Rabinoff, Zureick-Brown)

December 9: Lynnelle Ye. Uniform bounds for the number of rational points on curves of small Mordell-Weil rank, continued (Katz, Rabinoff, Zureick-Brown)

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

Organizers: Bjorn Poonen, Dhruv Ranganathan, Geoffrey Smith, and Isabel Vogt