SUMMER PROGRAM AT PRINCETON
Study Analysis and Geometry

Program Dates:  July 6 - July 22, 2011

Application Deadline:  April 15, 2011

Description
A three-week intensive program for 30 advanced undergraduates and 
beginning graduate students consisting of three related courses in 
analysis and geometry. Each course will consist of daily lecture(s) 
complemented by two-hour problem sessions each afternoon. On-campus 
accommodations and meal allowance provided from Tuesday, July 5 (checkin),
through Saturday, July 23 (check-out) as well as travel expense reimbursement

Eligibility:
Open to advanced undergraduates and beginning 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 who is well-
 acquainted with your academic work
 Official school transcript
 Personal statement, why you want to attend this program.  (Use 
 separate sheet or include on the online application.)

A brief description of the courses for summer 2011:

The Geometry of General Relativity
(G. Holzegel, Princeton University)

The main goal of this course is to introduce the peculiarities of 
Lorentzian geometry, in particular to understand the geometries of 
black hole spacetimes. We will take a pedestrian approach (exploring 
various geometries via their geodesics) to illustrate the general 
theorems that we are going to prove. Finally, we will connect our 
geometric insights to the study of partial differential equations on 
Lorentzian manifolds.

Discrete Analogues in Harmonic Analysis
(L. Pierce, Oxford University)
This course will survey a relatively new area of harmonic analysis: 
discrete operators modeled on classical operators, such as singular 
integral operators, maximal functions, fractional integral operators,
and Radon transforms. The classical operators are well understood, but 
their discrete analogues require new approaches, and in some cases 
remain rather mysterious. This course will offer a bird's eye view of
discrete operators and their classical counterparts and will introduce 
several techniques (stemming from number theory) for treating discrete 
operators.

Harmonic Analysis and Nonlinear Dispersive Equations
(A. Ionescu, Princeton University)
This course provides first an introduction to Fourier analysis, 
restriction theorems, Strichartz estimates, and =CE=9B(p) problems. We 
will then use these tools to study certain nonlinear dispersive models, 
such as semi-linear Schrodinger equations.

Please fill out online application at: www.math.princeton.edu/rtg/summer

Send all other required materials to:

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