IAS/Park City Mathematics Institute
The Graduate Summer School bridges the gap between a general graduate education in mathematics and the specific preparation necessary to do research on problems of current interest. Candidates should have completed basic graduate courses, including introductory courses in differential and algebraic geometry. Ideally, candidates will also have had some training in quantum mechanics, although this is not a prerequisite. In general, these students will have completed their second year and in many cases will already be working on a thesis. While a majority of the participants will be graduate students, some postdoctoral scholars and researchers may also be interested in attending.
The main activity of the Graduate Summer School will be a set of intensive short courses offered by the leaders in the field; these lectures will not duplicate standard courses available elsewhere. Each course will consist of lectures with problem sessions. Course assistants will be available for each lecture series.
This year's program is designed to introduce students of mathematics to some of the recent exciting interactions between mathematics and theoretical physics. In the first part of the program, a number of important topics in physics will be explained, largely from a mathematical perspective. These topics will be organized into three courses, covering classical field theory and supersymmetry, an introduction to quantum field theory, and an introduction to general relativity and supergravity.
Building on this foundation, the second half of the program will contain a course in mirror symmetry (largely from a physical perspective), and a multi-part course in the recent advances in enumerative geometry, many of which have arisen from the study of mirror symmetry and related topics. The second part of the program will also feature a series of presentations by experts in the field on a variety of topics. This may include lectures on mathematical problems of interest arising from string theory, reports from the research program on supergravity, panel discussions about the role mathematics plays in string theory and the role string theory plays in mathematics, etc. The precise nature of these presentations will depend on the participants.
Lecturers in the Graduate Summer School will include:
Course descriptions will be posted as they become available.
Participants in the Graduate Summer School also may wish to become involved in the Undergraduate Program, attend parts of the Research Program, or participate in the programs of the Education component. Graduate students are expected to participate in Institute-wide activities such as the "Cross Program Activities" and may be asked to contribute some time to volunteer projects related to running the Summer Session.
A limited number of graduate students who have not completed the basic courses may attend. These students will attend some graduate level courses and may be involved as teaching assistants in other programs or work as audio-visual assistants.
Application Guidelines and Forms