STAG: Students Teaching Algebraic Geometry.

STAG: Students Teaching Algebraic Geometry is a student-driven algebraic geometry discussion and learning seminar. We meet Wednesdays and Fridays at 10:00-10:30 in SCEN 349. The seminar is open to all mathematics students interested in algebraic geometry or related fields. Please come check us out!

Our format consists of short expository talks with questions encouraged, in addition to collaborative problem-solving sessions and presentations to prepare attendees to do mathematics research and give cogent talks. In the fall semester we learn the foundations of algebraic geometry and in the spring semester we transition into exploring interesting topics and open problems. The topics are attendee-guided, so participants are encouraged to suggest interesting directions and contribute.

On days where we present and discuss problems there will be pizza or other foods! Come with full minds and empty bellies.

Here is our calendar of topics and links to posted notes. NB: any links to posted notes may be works in progress and may be updated silently at any time without warning.

Date Speaker(s) Topic Notes
Wed 15 Sept Duncan Motivation for Algebraic Geometry Introduction to Algebraic Geometry §1 (pp. 1-2)
Fri 17 Sept Eric The Nullstellensatz Ibid. §2 (pp. 2-3)
Wed 22 Sept Eric Krull Dimension, Topologically Ibid. §2 (pp. 4-5)
Fri 24 Sept Duncan Motivation and Construction of Projective Space Ibid. §2 (pp. 5-6)
Wed 29 Sept Eric Affine Charts of Projective Space, Introduction to Presheaves Ibid. §2 (pp. 6-7), §3 (pp. 7-8)
Fri 1 Oct Duncan Sheaves, Localization of Rings Ibid. §3 (pp. 8-10)
Wed 6 Oct Eric Regular Functions and the Structure Sheaf on an Affine/Projective Variety Ibid. §3 (pp. 10-11)
Fri 8 Oct Duncan Sections and Stalks of the Structure Sheaf Ibid. §3 (pp. 11-12)
Wed 13 Oct Eric Objects and Arrows in the Category of Locally Ringed Spaces Ibid. §3 (pp. 12-14)
Fri 15 Oct Duncan §3 Cleanup, Equivalence between Varieties and Integral Domains over k Ibid. §3 (pp. 14-15)
Wed 20 Oct Eric Rational Maps Ibid. §4 (pp. 15-17)
Thurs 21 Oct Everyone Problem-Solving Session Pulled pork / jackfruit tacos
Fri 22 Oct Duncan Dominant Rational Maps, Birationality, and an Equivalence of Varieties Ibid. §5 (pp. 17-19)
Wed 27 Oct Eric Proving the Equivalence of Categories Ibid. §5 (pp. 19-20)
Fri 29 Oct Duncan The Case of Curves Silverman, The Arithmetic of Elliptic Curves §II.2 (pp. 19-21)
Wed 3 Nov Eric Motivation and Definition of Blowing Up ItAG §6 (pp. 21-23)
Fri 5 Nov Duncan Blowing Up, Continued, and Hironaka's Theorem Ibid. §6 (pp. 23-25)
Wed 10 Nov Eric Motivating Affine Schemes, Definition Part 1 Ibid. §7 (pp. 25-27), §8 (pp. 27-28)
Fri 12 Nov Duncan Examples and Morphisms of Affine Schemes, Definition Part 2 Ibid. §8 (pp. 30-33)
Wed 17 Nov Eric Affine Schemes of Any Ring, Equivalence of Categories Ibid. §8 (pp. 30-31, 33)
Thurs 18 Nov Everyone Problem-Solving Session Pineapple Thai curry
Fri 19 Nov Duncan Noetherian Schemes, Spectra of Finite Type k-Algebras Ibid. §8 (pp. 31-32)
Wed 1 Dec Eric Schemes Ibid. §9 (pp. 34-35)
Fri 3 Dec Eric Simplicial Objects and Homotopy Weibel, An introduction to homological algebra §8.1, 8.3 (pp. 254-257, 263-264)
Wed 8 Dec Everyone Plans for next semester None

For additional information or questions, contact Duncan at

Algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate. — David Mumford