Audience: 
Graduate Students
Undergraduates
Application Deadline
Sunday, April 15, 2012
Opportunity Text: 

SUMMER PROGRAM AT PRINCETON

Study Analysis and Geometry

Program Dates:  July 23 – August 10, 2012

Application Deadline:  April 15, 2012

A three-week intensive program for 30 advanced undergraduates and first-year graduate students consisting of two related courses in analysis and geometry. Each course will consist of nine lectures spanning 1.5 weeks. Daily lectures will be complemented by review and problem sessions.

On-campus accommodations and meal allowance provided from Sunday, July 22 (check-in) through Saturday, August 11 (check-out).

Travel reimbursement provided up to $500. (Only original receipts will be accepted.)

Early and/or extended stays are not permitted.

Courses

Harmonic Analysis: Some basic operators and the role of curvature
(A. Israel, Courant Institute/NYU and E. Stein, Princeton University)

Week 1 into Week 2: Monday, July 23 - Wednesday, August 1

The course provides and introduction to Fourier transform, Lp spaces, and several essential operators, such as the Hardy-Littlewood maximal function, fractional integrals, and singular integrals. This will be followed by a presentation of such topics as:
1. The Radon and X-ray transform
2. Spherical averaging operators and the corresponding maximal functions
3. Generalizations of the above where "non-vanishing" curvature plays a role
4. Restriction theorems

Nonlinear Evolution Equations
(A. Ionescu and S. Klainerman, Princeton University)

Week 2 into Week 3: Wednesday, August 1 - Friday, August 10

The course provides an introduction to applications of Fourier analysis to the study of certain nonlinear evolution equations. The course will cover the following topics:
1. Restriction theorems, Λ(p) problems, Strichartz estimates
2. Applications to nonlinear Schrődinger equations
3. Geometric wave equations and classical field theory
4. Applications to Yang–Mills and wave maps in the Minkowski space

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  

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

Requirements

• Complete and submit online application

• Letter of recommendation from faculty member or other well-acquainted with your academic work

• Official school transcript

• Personal statement on why you want to attend the program. (Fill out appropriate section on application or send separate PDF.)

For more information, please contact Jill LeClair, Program Coordinator, at leclair@princeton.edu.

Application

Fill out online application; all other supporting documents should be sent to:

Jill LeClair
Graduate Administrator
Department of Mathematics
312 Fine Hall
Princeton University
Princeton, NJ 08544-1000
leclair@princeton.edu