MAT 401: Undergraduate Seminar
Introduction to Enumerative Geometry

Stony Brook            Fall 2018


General Information, Notes on Conics, Notes on Grassmannians


You do not need to write up solutions to the discussion exercises, but it is essential that you work through them prior to the corresponding discussion session. Written solutions to the homework exercises are due at the beginning of the class on the due date. Late homework will not be accepted.

Tentative Schedule

Date TopicRead Homework
8/28, TuCourse overview and introduction Chapter 1 #1
8/30, Th
9/4, TuDiscussion of exercises
9/6, ThPlane curves and projective spaces Chapter 2 #2
9/11, TuEnumerative geometry of plane curves
9/13, ThDiscussion: plane conics
9/18, TuOverview of topology pp43-50#3
9/20, ThOverview of manifolds pp51-64
9/25, TuDiscussion: topology
9/27, Th Young tableaux and enumerative geometry by Aaron Bertram (University of Utah)
10/2, TuDiscussion: proof of Bezoit's Theorem
10/4, ThTransverse intersections pp64-88 #4
10/9, ThFall Break
10/11, ThOrientations and boundaries of manifolds
10/16, TuIntersection theory
10/18, Th
10/23, Tu Discussion: Grassmannians of two-planes
10/25, Th
10/30, Tu
11/1, ThLine bundles pp88-92
Chapter 7
Notes on
Vector Bundles
11/6, TuOperations on line bundles
11/8, ThVector bundles
11/13, TuOperations on bundles and applications
11/15, ThOverview of vector bundles
11/20, Tu Discussion: lines in projective spaces
11/27, Tu
11/29, ThA classical problem #6
12/4, TuDiscussion: Kontsevich's recursion for plane rational curves
12/6, Th Analogue of Kontsevich's recursion for real curves by Xujia Chen (Stony Brook)

This page is maintained by Aleksey Zinger.
Last modified: November 14, 2018.