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.
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
Austin Eide
Advised by: Xavier Perez
Nik Kuzmanovski
Advised by: Jamie Radcliffe
Meraiah Martinez
Advised by: Christine Kelley
Kirsten Morris
Advised by: Christine Kelley
Leilani Pai
Advised by: Xavier Perez
Jason Vander Woude
Advised by: Jamie Radcliffe and Vinod Variyam
Dan Welchons
Advised by: Christine Kelley
Recent Graduates
Emily McMillon (PhD 2022)
Advised by: Christine Kelley
Adam Volk (PhD 2022)
Advised by: Jamie Radcliffe
George Nasr (PhD 2021)
Advised by: Jamie Radcliffe
Alyssa Whittemore (PhD 2021)
Advised by: Xavier Perez
JD Nir (PhD 2020)
Advised by: Jamie Radcliffe
Allison Beemer (PhD 2018)
Advised by: Christine Kelley
Jessalyn Bolkema (PhD 2018)
Advised by: Judy Walker
Jessica DeSilva (PhD 2018)
Advised by: Jamie Radcliffe
Corbin Groothius (PhD 2018)
Advised by: Jamie Radcliffe and John Meakin
Rachel Kirsch (PhD 2018)
Advised by: Jamie Radcliffe
Carolyn Mayer (PhD 2018)
Advised by: Christine Kelley
Brent McKain (PhD 2017)
Advised by: Jamie Radcliffe
Charles Tomlinson (PhD 2017)
Advised by: Jamie Radcliffe
Caitlyn Parmelee (PhD 2016)
Advised by: Jamie Radcliffe
Sarah Behrens (PhD 2015)
Advised by: Stephen Hartke
Lauren Keough (PhD 2015)
Advised by: Jamie Radcliffe
James Carraher (PhD 2014)
Advised by: Stephen Hartke
Katie Haymaker (PhD 2014)
Advised by: Christine Kelley
Derek Boeckner (PhD 2013)
Advised by: Jamie Radcliffe
Katie Johnson (PhD 2012)
Advised by: Jamie Radcliffe
Katie Morrison (PhD 2012)
Advised by: Judy Walker
Derrick Stolee (PhD 2012)
Advised by: Stephen Hartke and N.V. Vinodchandran