Subject: FW: Graduate Summer School at Park City

From: "Croomes, Stacey V." <[email-masked]>
Date: Thu, 18 Jan 2007 15:25:27 -0800

-----Original Message-----
From: Scott Sheffield [mailto:[email-masked]] 
Sent: Thursday, January 18, 2007 3:08 PM
To: Croomes, Stacey V.
Subject: Graduate Summer School at Park City

Dear Stacey,

Would you be willing to forward the following letter to the mailing list
for mathematics graduate students at Caltech?  The letter describes a
graduate summer school at the Park City Mathematics Institute, organized
by Institute for Advance Study Princeton, that graduate students may
wish to apply to.  More info is available at

http://www.admin.ias.edu/ma/current/program.php

Many thanks!
Scott

*************************************************************

Dear Graduate Students:

I'm writing to encourage strong graduate students with interest in
probability and/or mathematical physics to apply to the graduate summer
school in Park City, Utah, from July 1 - July 21, 2007.

As you probably know, every summer IAS Princeton organizes a huge three
week mathematics event in Park City covering a major field of
mathematics. These events can have a large impact on the future of the
field.  We are very fortunate that this year's topic is probability and
statistical mechanics. The topic is timely, given that two of the
program principals --- Andrei Okounkov and Wendelin Werner --- received
Fields medals this year for related work. Some of this work will be
presented in the summer school courses.

Among other things, the Park City event features a research program
(with about 70 senior researchers) and a graduate summer school.  The
summer school will feature six courses (with roughly six lectures -- and
several TA-led problem sessions -- per course).  The instructors will be
David Brydges, Alice Guionnet, Richard Kenyon, Gregory Lawler, Yuval
Peres, and Wendelin Werner.  By any measure, this is a strong group of
instructors. Because the research program and summer school are held
together (and senior researchers often attend graduate courses, and
graduate students often attend research seminars), this is a good chance
for graduate students to get to know the senior researchers with whom
they will later apply to do postdoctoral work.

As you may know, Park City is a beautiful mountain resort town about a
half hour's drive away from the international airport in Salt Lake City.
(You may recall that it was the location of the skiing events in the
2002 Winter
Olympics.)  Program participants receive lodging in the same block of
housing and have catered lunches and breakfasts together every weekday.
The atmosphere is very conducive to intense research and study.  (See
www.parkcitymountain.com/summer/activities/index.html.) Feel free to
contact Catherine Giesbrecht <[email-masked]> if you have any
logistical questions or questions about the Park City area or about
funding details.

If you decide that you would like to come, then at some point before the
deadline of February 15, you should submit an application online at
http://www.admin.ias.edu/ma/current/application_gss_factsheet.php.  We
will make final decisions about program admission and funding offers
shorly thereafter.  We have sufficient funding to fully cover travel and
local expenses for up to 35 graduate students, and we may be able to
partially fund a larger group.  In past years, departments and advisors
with grants have made substantial contributions to student funding; if
the applicant pool is strong, there may be up to 70 funded students.

We will do everything we can to make the courses accessible to students
with minimal background (say, first year graduate courses in
probability, real analysis, and complex analysis). There will be a
variety of resources for students (such as lecture notes and TAs who
lead problem sessions and help with problem sets).

The Clay Senior Scholars in Residence (who will give accessible public
lectures) are Andrei Okounkov and Srinivasa Varadhan. Thomas Spencer and
I are the research program and graduate summer school organizers.

In the remainder of this email, I will very briefly describe the courses
themselves.  See http://www.admin.ias.edu/ma/current/program.php for
more complete (and far superior) course descriptions, as well as online
applications and other information.

Lawler and Werner will both address conformal invariance in two
dimensional statistical physics and will explain the work for which
Werner received the Fields medal.  Topics including the Schramm-Loewner
evolution (SLE), conformal field theory, critical percolation, and
random loop ensembles.

Kenyon will discuss the dimer model (including some of his joint work
with Okounkov).  This model has interesting connections to both
conformal field theory and algebraic geometry.

Brydges will introduce "renormalization," a far-reaching (Nobel-prize
winning) idea from the physics literature which is famously difficult to
make mathematically precisely, and explain some of the settings in which
it _is_ rigorously understood.

Peres will discuss determinantal point processes, and Guionnet will
discuss random matrix theory.  Although the courses will be quite
different, the topics are related to each other.  It turns out that the
eigenvalues of matrices chosen from certain natural probability
distributions have laws that are naturally described using determinants;
these laws are "universal" in the sense that they crop up (sometimes
provably, sometimes experimentally) all over the place in science and
mathematics.

Best wishes,

Scott Sheffield
Courant Institute, New York University
Institute for Advance Study Princeton