Summer Program in Princeton

Study Analysis and Geometry

Program Dates: Monday, July 27–Friday, August 14, 2009

Application Deadline: April 15, 2009

Description

A three-week intensive program for up to 25 mathematicians consisting of three related courses in analysis and geometry. Each course will be comprised of eight one-hour lectures. The main lectures will be complemented by two-hour problem sessions each afternoon conducted by graduate students within the department.

On-campus accommodations and meal allowance provided from Sunday, July 26, through Saturday, August 15, 2009.

Travel assistance may be available to U.S. candidates by request and on a case-by-case need. (Only original receipts will be accepted for reimbursement purposes.)

Courses

Introductory Topics in Fourier Analysis

(E. Stein, Princeton University)

After a quick introduction of the basic facts concerning the Fourier transform on R^d we turn to: smoothness and Sobelev spaces; oscillatory integrals and van der Corput estimates; curvature of hyper-surfaces and Fourier transform of surface-carried measure; and applications to restriction theorems.

Several Complex Variables and Partial Differential Equations

(A. Nagel, University of Wisconsin)

This will be an introduction to complex analysis in several variables. We will examine some of the new phenomena, such as the Hartogs extension theorem, that appear when studying holomorphic functions of two or more variables. We will also see how the construction of holomorphic functions with desired properties is related to existence and regularity results for systems of partial differential equations. In particular, we will formulate and discuss the ∂-problem and the ∂-Neumann problem.

Partial Differential Equations in Geometry

(G. Tian, Princeton University)

This will be an introduction to Geometric PDE and geometric analysis. We will start with basic notions in differential geometry, connections, and curvature. We will discuss how geometric PDE and analysis can be applied to studying geometry and topology of underlying manifolds. In particular, I will show the geometrization of 2-dimensional manifolds.

Eligibility

• Open to currently enrolled juniors and seniors and first-year graduate students, with priority given to undergraduates

• Must be a U.S. citizen or permanent resident [see note below]

• Applicants will be considered without regard to race, color, religion, sex, sexual orientation, age, ethnicity, or disability

NOTE: Consideration may be made for a limited number of international students. If accepted, the student must pay all of his or her own expenses.

Requirements

• Complete and submit online application

• Two letters of recommendation from faculty members or others well-acquainted with your academic work

• Official school transcript

• Personal statement of why you want to attend the program. Use separate sheet or include on online application.

For more information, please contact Jill LeClair, program coordinator, at leclair@princeton.edu.

Application

Fill out an online application; all other application materials should be sent to:

Jill K. LeClair
Graduate Administrator
Department of Mathematics
307 Fine Hall
Princeton University
Princeton, NJ 08544-1000