# Research Opportunities for Undergraduates

## Research at W&L

Students can sometimes start or continue doing research during semester with faculty here at W&L. Anywhere from 1-3 credits can be awarded for this work. It's usually best to contact the faculty member directly to discussion your options with them.

## Summer Research at W&L

Students can spend the summer doing research with faculty at W&L. The Summer Research Scholars program provides funding for students.

- Note that the SRS application deadline is generally around Thanksgiving break of the Fall term prior to the summer you want to do research.
- For information on how to apply click here.

Meet the mathematics faculty and read about some of their research projects.

**Aaron Abrams**conducts mathematical research on several different topics, overlapping the traditional boundaries of geometry, topology, group theory, combinatorics and probability. Currently, his main interest is tilings of a square, by triangles or rectangles.**Kevin Beanland's**research area is Banach space theory. His recent research include some aspects of real analysis and how descriptive set theory as it applies to Banach space theory. In particular, he studies study the geometry of infinite dimensional Banach spaces and bounded linear operators between Banach spaces. Most of his work has focused on constructing Banach spaces with very rigid structure and using methods from descriptive set theory to study operators between Banach spaces.**Michael Bush**works on problems arising from the interactions between algebraic number theory, Galois theory and group theory. He's supervised undergraduate projects on various topics with an algebraic flavor. Recent projects have focused on understanding the periods and other properties of sequences defined by recurrences over finite algebraic structures.**Cory Colbert's**primary research area is commutative algebra. While his research interests are ever-broadening, he currently has a particular interest in understanding the prime ideal structure of commutative Noetherian rings, and how answering questions arising from that can help produce constructions of interest in other related areas.**Elizabeth Denne**is interested in geometric knot theory. She uses topological knot invariants to answer questions about the geometry of knots. For example, how much bend or twist does a knot have? How much length of rope is needed to tie a knot? Recent research projects include the mathematics of tie knots and folded ribbon knots.**Gregory Dresden****'s**research area is number theory, continued fractions, and Fibonacci numbers. His current work is on looking for patterns in polynomials and their roots when expressed as continued fractions; it's a nice combination of topics from abstract algebra and number theory.**Wayne Dymacek**has advised many students on research projects in graph theory and combinatorics.**Nathan Feldman's**research is in the areas of operator theory, complex analysis, and chaotic infinite dimensional dynamical systems. This lies at the cross roads of infinite dimensional linear algebra, analysis, and unpredictability**Stephen Hardy**applies continuous logic and ultraproducts to C*-algebras.**Carrie Finch-Smith**studies number theory, specifically in covering systems and irreducibility of polynomials and questions regarding Sierpinski numbers using coverings of the integers.**Alan McRae's**research area is spacetime geometries and geometric probability.

## Summer Research Elsewhere

There are opportunities for summer research in mathematics at other institutions.

- The American Mathematical Society has a list of many of these programs here.
- The National Science Foundation also has a list of summer research programs here.
- Dr sarah-marie belcastro has an excellent page all about summer research opportunities.

Note that most REUs receive many many more applications than they have spots, so it's a good idea to apply to at least 6 of them. They also vary widely in structure (for example, whether students work individually or in groups, on similar projects or different projects, with lots of faculty supervision/interaction or very little). If you've been accepted to more than one REU, be sure to ask about the details of the structure if these aspects of your working environment are important to you.