Welcome to Math 259!
Course description:
How many geometric objects of a given type satisfy given geometric conditions?
For instance, one may ask forIn many cases, this comes down to calculating intersection numbers on moduli spaces.
In the first part of the course, we will discuss Chern classes and show some of their applications to enumerative questions.
In the second part, I will give an introduction to the moduli space of curves. In particular, I hope to include a discussion of the Quot scheme, of geometric invariant theory, outline the construction of the moduli space, and possibly calculate one or two concrete intersection numbers.
(This may be a bit too ambitious for a one quarter course, so the goals may change slightly as we go.)
Instructor: Dragos Oprea, doprea "at" math.you-know-where.edu, AP&M 6-101.
Lectures: MWF, 12pm-12:50pm, TBA.
Office hours:
I am available for questions after lecture or by appointment. Also, feel free to drop in if you see me in my office.
Prerequisites:
Lecture Summaries