DOmath
is fulltime 8 week program for
collaborative student summer research in all areas of mathematics.
This
program is open to undergraduates at Duke only; all Duke undergraduates are encouraged to apply. The program consists of groups of 23 undergraduate students working
together on a single project. Each team will be led by a faculty
mentor assisted by a graduate student.
Participants
will receive a $4,000 stipend, out
of which they must arrange their own housing and travel.
Funding and infrastructure support are provided by Department of
Mathematics and Office of Undergraduate Affairs at Duke
University. Participants
may not accept employment or take classes during the program.
The
program runs from May 22 until July 14, 2017. The application
deadline is February 20, 2017 with teams expected to be finalized by
March 1. Applicants will be notified about the decision by email no
later than March 10.
There
are four teams planned for summer 2017 in the numbered list below.
Please indicate the number of the projects you choose when you apply;
you may list up to four choices in ranked order of preference. For each of your choice of projects, a short explanation of why you have chosen them and how you feel you could contribute to them.

Simulations
of Spiral Galaxies,
led by Professor Hubert
Bray
As
most of the gravity inside galaxies is not due to visible matter,
astronomers have become convinced that galaxies are mostly made out
of invisible matter, called dark matter. In this project, students
will use Professor Bray's spiral galaxy simulator, tweaking it as
necessary, to test ideas about the nature of dark matter and the
role it plays in spiral patterns in galaxies.

Rational
points in orbits of matrix groups,
led by Professor Jayce
Getz
A
classic problem in number theory is deciding whether a system of
polynomial equations with coefficients in the rational numbers has a
solution in the rational numbers. In this project we will be
investigating this question for a family of cases that arise
naturally in the context of actions of matrix groups.

Laplacian
eigenfunctions and interacting particles,
led by Professors
Jianfeng Lu and
Jim Nolen
We
study algorithms based on random walkers for approximating the
eigenfunctions of the Laplacian and their nodal sets. Such
algorithms have applications in spectral graph theory and
computational quantum mechanics.

Random
fragmentation,
led by Professors Matt
Junge and
Jim Nolen
We
will study random algorithms that spread points in various spaces,
such as the unit interval, box, and sphere. The project involves
both rigorous analysis and implementation of these algorithms.
Understanding these algorithms relates to Problem 7 of Stephen
Smale's "Problems for the next century."
