Stanford Undergraduate Research Institute in Mathematics
June 23-August 29, 2014
The Stanford Undergraduate Research Institute in Mathematics
is a ten-week program that provides Stanford undergraduates
the opportunity to work on mathematical problems in an
extra-curricular context. Most students will work on interesting
mathematical problems in a collaborative environment. A number will
work one-on-one with faculty member. Summer funding will be
available for some students, thanks to VPUE; others can obtain
course credit in the fall quarter for participating.
You can find the SURIM 2012 website here and SURIM 2013 website here .
Individual Research with a Faculty Member
Students working individually with a faculty member will decide on a project
and the dates in consultation with their faculty mentor. Note that it is
the duty of the student to find a faculty member interested and willing to work with
them. A short project proposal will be requested with the application.
students will take part, full-time, in the ten-week program that will run from Monday, June 23 through Friday, August 29.
Goals of the program
At SURIM, students will be exposed to questions that are
of interest in current mathematics, as well as the research and
exploration aspects that accompany such questions. With their
mentor's assistance, students will study the prerequisite materials to
understand their program's topic and will then participate in
exploration of their questions about the subject. The emphasis will be
on self-discovery of examples and properties. In addition to knowledge
of their subject and an understanding of what it means to explore a
research question, participants will practice the
ability to present mathematics in a formal seminar setting, use
software such as LaTeX to typeset mathematics, use other programming
languages to study mathematical questions, and interact
with peers, graduate students and faculty.
All Stanford students who will be enrolled full/part-time during the Fall of 2014 are eligible to apply.
Format for the ten-week program
Students will be divided into groups depending on their mathematical
interest and background. Each group will work closely with graduate
A typical week
There will be a couple of formal meetings with mentors each week. At
the start, the mentors will lay out the beginning of the project, and
the groups will decide how best to begin. Each group will prepare
presentations to the entire institute each week, giving a status
report to those working on other problems. (Practice with getting
across ideas is essential to doing mathematics!)
Much of the week will be spent working individually and in groups, and
in informal discussions with mentors.
There will be roughly two additional events per week. Some will be
introductions to research tools (from writing with LaTex to the use of
various software packages). Others will be lectures from researchers in
academia and industry on what research is actually about --- how it is
done, how to do it, and what it is like. Please check back for the schedule.
group will also have access to various classrooms during the summer, which will be listed later in the year.
The calendar for the summer is available here. This link also includes information about workspace available to the groups.
We are still working on choosing the projects for the summer.
Below are two of the projects students will be working in 2014.
Random Walks On Finite Groups - Card Shuffling (mentor: Evita Nestoridi)
One of the main questions concerning a random walk on a finite group is finding
the order of the mixing time of the walk. In particular, in card shuffling
we are really interested in finding out how many shuffles are required to get
the deck "perfectly" shuffled. In this project, we are going to learn techniques
of bounding the mixing time and play with a lot of examples. We will try to
actually solve particular problems-examples either from card shuffling or from a
group of matrices over a finite field (or perhaps another finite group that we might
find interesting) and ideally come up with new techniques for bounding the mixing
What happens when we iterate polynomials on the projective line?
(mentor: Niccolo' Ronchetti)
Suppose you take a polynomial f(z), say with rational coefficients. You
can try to iterate the polynomial: z -> f(z) -> f(f(z)) -> ? What happens
to the orbit of some z? Is it periodic, or maybe dense? Does it contain
infinitely many primes? More generally what arithmetic properties do the
set of periodic points have? There are plenty of interesting questions
that one can ask and try to figure out. We will try to explore them and
learn plenty of exciting math in the process (for example we'll learn
about Galois groups, Diophantine problems, local fields?)
What is the shape of molecule space? Can we develop topological OCR? (mentor: Ryan Lewis)
Topological data analysis attempts to extract a topological
understanding of scientific data from
finite sets of samples. Usually data analysis assumes that the input
is a point cloud
and comes from some underlying geometric space. Topological data
analysis focuses on
the recovery of the lost topology of this underlying space. For this
project we are looking for students to do topological data analysis.
We will use a new computational topology library to analyze data sets.
For those less interested in using and writing software, more
mathematical problems can be solved.
Please submit the following information, by email, to Nancy Rodriguez at firstname.lastname@example.org, by March 1, 2014 with subject line ''SURIM application''. Please include in the email the following information:
- (a) Name, Stanford ID number, and year.
- (b) If you have a faculty member who has agreed to work one-on-one with you, please let us know. (This is not necessary to apply.) If this is the case, please include a short proposal, developed in consultation with your intended mentor.
- (c) Name of one or two professors who are familiar with you
(ideally in mathematics)
- (d) Mathematical background and interests.
- (e) For those not working individually with a faculty member, which of the
possible projects appeal to you? (we are still working on project 3…if geometry and topology intestes you state that on your application)
- (f) Do you need funding in order to take part? Would you like course credit? (Note: it is not possible to get both funding and credit.)
- (g) Curriculum vitae and unofficial Stanford transcript.
Notification Deadline: Students will be notified of their acceptance
by March 15, 2014.
Directors: Gunnar Carlsson and Chris Henderson. Assistant Director: Ravi Vakil.
If you have any questions, or are even just curious about the program,
please contact Chris Henderson (chris -at- math.stanford.edu).