For the faculty members whose main focus is teaching undergraduate students, PCMI offers the opportunity to renew excitement about mathematics, talk with peers about new teaching approaches, address some challenging research questions, and interact with the broader mathematical community. Each year the theme of the UFP bridges the research and education themes of the Summer Session.
The 25th Annual PCMI Summer Session will be held June 28 – July 18, 2015.
Click HERE to apply to the Undergraduate Faculty Program.
Dagan Karp, Harvey Mudd College
"Out of Many, One: An Introduction to Moduli"
Moduli spaces and representation theory are responsible for some of the most beautiful and important mathematics and theoretical physics to be developed in the last 30 years. Related fields include topology, geometry, combinatorics, number theory, dynamics, quantum field theory, and string theory. Modular interpretations of classical geometric objects have provided deep insight. Representation theory has opened up new avenues of study in number theory. Specific subdisciplines include Gromov-Witten theory and the Langland’s program, related to the research of the Clay Senior Scholars in residence at PCMI 2015.
How can we teach this new and technical material to undergraduates? How do we conduct research in these areas with undergraduates? We will pilot such a course in the Undergraduate Faculty Program, with participants involved in course development at all levels. We will also discuss research projects, guided by papers in these areas co-authored by undergraduate students. Our goal is to provide a friendly introduction, preparing participants to teach such a course and guide their students toward research.
We will primarily be focused on such basic objects such as the moduli space of curves (Riemann surfaces) and representations of the symmetric group, which are deeply related. We may also explore moduli of maps, tropical curves and other subjects depending on interests of the participants. We will specifically study prerequisite material, as would be needed by an undergraduate student, so prior knowledge of these subjects is not required. All interested faculty are warmly encouraged to apply.