Reading Seminar on Intersection Theory, Fall 2018

Organized by Noah Olander and Song Yu at the Department of Mathematics, Columbia University

Time and location: Thursdays 2:30-4:00pm, 507 Mathematics

The goal of this reading seminar is to learn intersection theory in the style of a topics course. We will mostly follow William Fulton's classical book Intersection Theory. We will first go over the foundational setup of the subject (Chapters 1-8 of Fulton), and then move on to a selection of more involved results and applications from the remaining chapters and literature.

Please email the organizers if you wish to join the mailing list.

Special thanks to Henry Liu and Michael Zhao for live-TeXing notes for the seminar. Here are Henry's notes and here are Michael's notes.

References and Resources

Schedule

Date Speaker Title Reference
Sept 13 Song Yu Rational Equivalence §1
Sept 20 Noah Olander Divisors §2
Sept 27 Alex Pieloch Vector Bundles and Chern Classes §3
Oct 4 Song Yu Cones and Segre Classes §4
Oct 11 Renata Picciotto Deformation to the Normal Cone, Intersection Products §§5, 6
Oct 18 Reading, Review, Discussion
Oct 25 Noah Olander Intersection Multiplicities §7
Nov 1 Adam Block Intersections on Nonsingular Varieties §8 [Notes ]
Nov 9 Henry Liu Excess and Residue Intersections §9
Nov 15 Song Yu Grassmannians, Schubert Calculus §14
Nov 22 Thanksgiving - no seminar
Nov 29 Yakov Kononov Grothendieck-Riemann-Roch Theorem §§15,18
Dec 6 Carl Lian Intersection Theory on Moduli Spaces of Curves [L], [M]
Dec 14 Carl Lian Intersection Theory on Moduli Spaces of Curves (cont'd) [L], [M]