Research interests in this group center around structural problems in combinatorics, and coding theory, the study of schemes for encoding data to, for example, efficiently detect errors in transmission.

Faculty

Stephen Hartke works in discrete mathematics, primarily graph theory, but also combinatorics, probability, and discrete optimization. He is interested in applications of discrete mathematics, particularly to biology and computer science.

Mitch Keller works in combinatorics, with a particular interest in the combinatorics of partially ordered sets. His research includes connections to computer science through online algorithms and commutative algebra in the form of Stanley depth for monomial ideals.

Christine Kelley works in coding theory and applied discrete mathematics. Her focus is on the analysis and construction of graph-based codes and the relationship between the graph representation of a code and its decoding performance. While much of her work is on LDPC codes, she is also interested in applying these techniques to other codes and problems in engineering.

Jamie Radcliffe works in several areas of combinatorics, discrete mathematics and geometry. His most recent work is on reconstructibility—reconstructing a geometric object from knowledge of its smaller pieces.

Judy Walker works in algebraic coding theory. Much of her work uses techniques from number theory, algebraic geometry and graph theory. She has worked with algebraic geometric codes over rings and the relationship between weight measures on these codes and exponential sums. Currently, she studies low density parity check codes, focusing especially on their pseudocodeword structure.

Graduate Students

Sarah Behrens Stephen Hartke

Derek Boeckner Jamie Radcliffe

James Carraher Stephen Hartke

Katie Haymaker Christine Kelley

Katie Johnson (PhD 2012) Jamie Radcliffe

Lauren Keough Jamie Radcliffe

Katie Morrison (PhD 2012) Judy Walker

Derrick Stolee (PhD 2012) Stephen Hartke and N.V. Vinodchandran