Discrete Mathematics and Coding Theory

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

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.

Tri Lai works in algebraic and enumerative combinatorics. He is currently focusing on tiling problem and related topics, including alternating sign matrices, plane partitions, statistical physics, cluster algebras, electrical networks.

Kyungyong Lee is interested in algebraic geometry, algebraic combinatorics, cluster algebras, commutative algebras, non-commutative algebras, representation theory, and mathematical physics. His research lies in the intersection of commutative algebra, algebraic geometry, and discrete mathematics.

Xavier Pérez-Giménez works in probabilistic combinatorics. Much of his research concerns the study of random graphs and related combinatorial structures that involve probabilistic ingredients. While his focus is primarily theoretical, some of his work has practical applications in other fields such as computer science. Finally, he is also interested in the analysis of infection/information dissemination processes such as bootstrap percolation.

Jamie Radcliffe works in several areas of combinatorics, discrete mathematics and geometry. His most recent work is on extremal problems for enumerative graph parameters--parameters of a graph obtained by counting the number of substructures of a certain type in the graph.

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.

Current Graduate Students

Allison Beemer
Advised by: Christine Kelley

Jessalyn Bolkema
Advised by: Judy Walker

Jessica DeSilva
Advised by: Jamie Radcliffe

Corbin Groothius
Advised by: Jamie Radcliffe and John Meakin

Rachel Kirsch
Advised by: Jamie Radcliffe

Brent McKain
Advised by: Jamie Radcliffe

Carolyn Mayer
Advised by: Christine Kelley

Charles Tomlinson
Advised by: Jamie Radcliffe

Recent Graduates

Sarah Behrens (PhD 2015)
Advised by: Stephen Hartke

Derek Boeckner (PhD 2013)
Advised by: Jamie Radcliffe

James Carraher (PhD 2014)
Advised by: Stephen Hartke

Katie Haymaker (PhD 2014)
Advised by: Christine Kelley

Katie Johnson (PhD 2012)
Advised by: Jamie Radcliffe

Lauren Keough (PhD 2015)
Advised by: Jamie Radcliffe

Katie Morrison (PhD 2012)
Advised by: Judy Walker

Caitlyn Parmelee (PhD 2016)
Advised by: Jamie Radcliffe

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