The
instructor for the course is
me, Jim Bryan

This course is an introduction to modern enumerative
algebraic geometry. It is largely concerned with
quantum invariants coming from "curve counting" in
various guises. "Quantum invariants" in this context
is a catch-all phrase referring to deformation
invariants constructed in algebraic geometry which are
mathematical analogs of quantities arising in string
theory. The invariants we will consider are Gromov-
Witten invariants (including quantum cohommology),
Donaldson-Thomas invariants, Pandharipande-Thomas
invariants, and Gopakumar-Vafa invariants. They can
all be regarded as theories which provide virtual
counts of curves on a Calabi-Yau threefold. We will
study the structure which underlies these invariants
and the various relationships (many of which are
conjectural) between the invariants as well as
techniques for computing these invariants.

The class meets in MATH 102 on MWF
from 1:00pm to 2:00pm

I will post my lecture notes here. I will update this as the term progresses. Lectures 1-6, Lectures 7-14 , Lectures 15-19 , Lectures 20-32 , Lectures 33-34 , Lectures 35-40 ,

A good overview is the paper 13/2 ways to count curves by Pandharipande and Thomas. The references within this paper provide an excellent guide to the literature.

Homework will
assigned sporatically.

Students will do an end of the term project which could be written or presented.

Here is Homework 1. Solution to HW1 Problem 3 is here.

Here is Homework 2a.

Here is Homework 2b.

Here is Homework 3a.

Here is Homework 3b.