Department of Mathematics, Duke University

Program ID: Duke-DOMATH [#529]
Program Title: DOmath
Program Type: Undergraduate program
Program Location: Durham, North Carolina 27708-0320, United States [map]
Subject Area: Mathematics
Starting Date: 2017/05/22
Application Deadline: 2017/02/20 (posted 2016/12/31, updated 2016/12/27)
Program Description:    

*** the list date or deadline for this program has passed, and no new applications will be accepted. ***

DOmath is full-time 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 2-3 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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."


Application Materials Required:
Submit the following items online at this website:
And anything else requested in the program description.

Further Info:
https://math.duke.edu/DOmath
 
Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320

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