DOmath (Duke Opportunities in Mathematics) is a new summer research program in mathematics at Duke, starting in summer 2017. It will last for eight weeks from May 22 to July 14, 2017. The stipend per student is expected to be $4000 for the summer. This program is open to all Duke undergraduates.
DOmath is a program for collaborative student research in all areas of mathematics. The program consists of groups of 2-3 undergraduate students working together on a single project. Each team will be led by a faculty mentor assisted by a graduate student. This program is intended to complement our current PRUV program, which is aimed at facilitating research by individual students (usually rising seniors) under the mentorship of a faculty member.
For the 2017 program, there will be four DOmath teams:
- 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."
Apply for DOmath via DOmath2017. The deadline for the application is February 20, 2017, with teams expected to be finalized by March 1, 2017. If you are interested in participating in the program and want to receive updates on the application process, please email Heekyoung Hahn (firstname.lastname@example.org) to be added to the mailing list for DOmath. If you have questions, please email Lenhard Ng (email@example.com) or Heekyoung Hahn (firstname.lastname@example.org) for information.