Summer Research in Mathematics & Computation

Our summer 2013 REU is canceled. Thank you for your applications.

The Bard College REU in Mathematics & Computation is an eight week summer program in which undergraduates work in groups with individual faculty members on active and current research projects in pure and applied mathematics, mathematical physics, and mathematical computation. Throughout the summer, students will be exposed to theoretical constructs, computational techniques, and real world applications, and they will develop the background and skills to prepare them for further study or employment in a mathematics-related career. The REU will also provide workshops on LaTeX, Sage, Matlab, and other mathematical software.

Bard College is situated on over 500 acres along the Hudson River, 90 miles north of New York City (Campus Map and Tour). Workshops, seminars, and lectures will held in the state-of-the-art Gabrielle H. Reem and Herbert J. Kayden Center for Science and Computation, opened Fall 2007, and students will be provided space in a dedicated computer lab. REU participants will be part of a summer research community of dozens of students, with regular social events.

Participating students will receive a stipend of $4000, free double-occupancy on-campus housing, and up to $800 in travel expenses. This financial support and free housing is available only to U.S. citizens or permanent residents.

Please email questions to mathreu@bard.edu. (This address is NOT for submitting application materials or letters of recommendation. We will NOT read any such materials or letters sent by email or postal mail. All application materials and letters of recommendation MUST be submitted via MathPrograms.org.)

Eligibility

We welcome applications from both current sophomores and juniors, including students who have decided to major in mathematics as late as their junior year and students who are undecided about a career in mathematics. Applicants must not yet have graduated with an undergraduate degree at the time of the REU.

Women and underrepresented groups are particularly encouraged to apply.

Due to National Science Foundation restrictions, financial support is available only to U.S. citizens or permanent residents. Students who are not eligible for financial support are still welcome to apply, provided they can obtain alternative funding from their home institution or another source.

In physics, supersymmetry is a pairing between bosons and fermions appearing in theories of subatomic particles. To study supersymmetry, Faux and Gates recently introduced Adinkras, graphs with vertices representing the particles in a supersymmetric theory and edges corresponding to the supersymmetry pairings.

Although Adinkras arise in the study of supersymmetric physics, participants will study them from a pure mathematics point of view, starting with their basic axioms. In graph-theoretic terms, Adinkras are N-regular, edge N-colored bipartite graphs with heights assigned to the vertices and signs assigned to the edges, satisfying various conditions. Adinkras are closely related to Clifford algebras, and we have recently discovered that the underlying graph of an Adinkra is actually the Schreier coset graph corresponding to a doubly-even linear binary error correcting code. Participants will study Adinkras from various points of view, including graph theory, linear algebra, abstract algebra, and coding theory. Also, participants will be enlisted in the ongoing project of classifying the simplest examples of Adinkra graphs, using computational software such as Sage and Mathematica as necessary.

Prerequisites: Linear Algebra and an introductory proofs-based course. Students must also have at least one of the following: Abstract Algebra, Combinatorics, Graph Theory, Coding Theory, or computer programming experience. No background in physics is required.

Topics in Discrete Geometry

Students will work on one of two different projects, depending on their backgrounds and interests.

Combinatorial Aspects of Bivariate Splines
A bivariate spline is a piecewise polynomial function whose domain is a region of the plane broken up into triangles. What types of splines can occur depends on the number of triangle and how they fit together.

Voronoi Diagrams and Delaunay Tessellations
The goal of this research is to explore geometric and combinatorial properties of Voronoi diagrams, their Delaunay tessellations, and their underlying graphs.

Prerequisites: Multivariable Calculus, Linear Algebra, an introductory proofs-based course, and at least one upper level proofs-based course. Computer programming experience and a course in Abstract Algebra, or Combinatorics, or Graph Theory is helpful but not required.

Gerrymandering: Theory and Practice

In the United States and other modern democracies, voters are partitioned into legislative districts, and the voters within a district elect someone to represent them in the legislature. Gerrymandering is the practice of dividing the districts in such a fashion as to give one political party an unfair advantage.

The ultimate goal of this research is to derive measures of district shape that can be used to assess districting plans, with an eye towards practical utility (e.g., incorporating such measures into evaluations of districting plans by both legislatures and the courts). There are several directions this research might take: