IAS/Park City Mathematics Institute
The Undergraduate Program 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. Based on the backgrounds of the accepted students, they will be divided into two groups - introductory and advanced. There will be several activities organized for these groups, with some specifically intended for either the introductory or advanced group. There will be time for study groups and individual projects guided by advisors, as well as other activities.
The undergraduate program for Summer 2001 will present topics selected for their intrinsic interest, and for their value as background for the research and graduate programs. The lead lecturer for the undergraduate program will be Sheldon Katz of Oklahoma State University. His course will present an introduction to enumerative geometry and its connections with mathematical physics. A second course will treat the fundamentals of differential geometry from a modern point of view.
Lecturers for the Undergraduate Program:
This course will introduce what is perhaps the most famous example of how ideas from physics have revolutionized mathematics: string theory has led to a complete overhaul of enumerative geometry, an area of mathematics started in the 19th century. Century-old problems of enumerating geometric configurations have now been solved using new and deep mathematical techniques inspired by physics!
The physics content of the course will focus on explaining the action principle in physics, the idea of string theory, and how these directly lead to questions in geometry. The bulk of the course will focus on the development of the mathematical techniques to approach these questions, based on a blend of algebra, geometry, and analysis.
Introduction to Differential Forms and Differential Geometry
This course will provide an introduction to differential geometry and to the language of differential forms. General ideas will be illustrated by a selection of concrete, computable examples.
The course will begin by reviewing multivariable calculus and introducing the language of differential forms. These ideas will then be used to discuss differentiable manifolds, which will form the basis for consideration of complex geometry, topology, matrix groups and related topics.
The course should be accessible to students with a firm grasp of multivariable calculus and linear algebra.
This page last updated December 13, 2000
questions or concerns should be directed to C. Giesbrecht