Undergraduate Summer School 2015

The Undergraduate Summer School provides opportunities for talented undergraduate students to enhance their interest in mathematics. This program is open to undergraduates at all levels, from first-year students to those who have just completed their undergraduate education. There will be many organized activities, with some specifically targeted at students at the introductory level and others at more advanced students. There will also be time for study groups and individual projects guided by advisors, as well as other activities.

The 25th Annual PCMI Summer Session will be held June 28 – July 18, 2015.

Click HERE to apply to the Undergraduate Summer School program. 

2015 Course Description:

Algebraic Geometry has been at the heart of much of mathematics for at least two hundred years. It has influenced a tremendous amount of modern mathematics, ranging from number theory to robotics. As Algebraic Geometry uses tools from almost all areas of mathematics, it is not an easy area to enter. The Undergraduate Summer School will provide an introduction to some of the current issues in modern algebraic geometry. There will be three parts to the summer school.

First, each participant will work on an individual project, whose topic will be chosen in consultation with the two UGSS lecturers, for the three weeks of the institute. These projects could range from the writing of expositions on topics in algebraic geometry to working on open problems.

Second, Aaron Bertram (University of Utah) will be giving daily lectures on Algebraic Geometry: Flag Varieties and Representations. The goal of these lectures is to introduce the varieties of flags of linear subspaces, see how they are built, what their equations look like, and how they are machines for producing representations of algebraic groups.

Third, Tom Garrity (Williams) will be giving daily lectures on Algebraic Geometry: Moduli Theory and Invariants. The overall topic for these lectures is to try to understand what it should mean for two geometric objects to be the same. This simple question leads to much of current algebraic geometry. These lectures will start with the subject of classical invariant theory and then outline how to attempt to construct moduli spaces.

There will be a lot of other mathematics going on at PCMI.  Participants in the UGSS  will have the chance to meet and interact with mathematicians and math teachers from around the world. The Undergraduate Summer School is for all undergraduates or recent graduates. The only prerequisite is a course in abstract algebra.


The Coordinators of PCMI’s Undergraduate Summer School are Steven Cox, Rice University, and Thomas Garrity, Williams College.