Participating Faculty Members
Updated for 2015
Dr. Sandy Fillebrown
Fractals and Iterated Function Systems
Dr. Rachel Hall
My research is in both applied mathematics (quantitative analysis of music) and musicology (study of American folk hymns). Folk hymns originate in the oral tradition of sacred song. They were first published in the 19th century, primarily in shape-note notation. Over generations and without written music, churches had developed their own versions of common tunes. Additional variations appeared through transcription and arrangement. I aim to propose a classification of tune resemblance, develop quantitative measures of distance that identify variant melodies, and explore the possibility of using these measures to identify tune families and folk hymn “archetypes,” or compositional strategies. I am willing to advise a student in either field, but prefer that students have some experience or interest in both. In particular, students should be able to read music. Students will also have opportunities to develop their practical music skills by learning to sing shape-note music. Programming experience is a plus.
My fields of research are combinatorics and graph theory. In very general terms, combinatorics deals with enumeration of the number of ways to perform a mathematical task (such as choosing a delegation of three people to represent a group of 15 people), and graph theory is concerned with diagrams you make by connecting dots with lines. Since these areas are relatively accessible to undergraduates, they are often sources of undergrad-level research problems, but not all the projects I have directed have been purely combinatorial, because the choice of topic is in large part driven by the student’s needs and interests. I have directed projects each of the last five summers. In ’06, I directed two summer scholar projects: The role of invariance in mathematics (which, among other things, investigated the use of an invariant in a number of combinatorial problems) and Generalized Möbius Inversion (which is abstract combinatorics). In Summer ’07, I directed a project in another area of combinatorics, Pólya-de Bruijn Theory, which deals with enumeration questions in which not all the ways of performing a task count as different. (For example, consider painting the faces of a cube using k colors. Rotating the cube will make some colorings coincide with others.) I directed a project centered on probability theory in ’08, on stochastic processes and the Black-Scholes formula in ’09, and on problem solving in ’10. For more details on these projects, please see the one-page summaries prepared by the students.
Dr. Rommel Regis
My main research area is Mathematical Optimization, which focuses on the development of algorithms for finding the maximum or minimum of a function of several variables, possibly subject to some constraints. This research area has a wide range of scientific, engineering (aerospace, mechanical, industrial, environmental), business and medical applications. To begin research in my field requires some background in Multivariable Calculus, Linear Algebra and knowledge of a programming language. For a listing of my publications, please check out my Google Scholar profile: http://scholar.google.com/citations?user=CeNcWNgAAAAJ&hl=en