Areas of Interest
Combinatorics, graph theory
Research
My research is in combinatorics, especially matroids and their connections with combinatorial geometry and graph theory. The main topic of my work is signed, gain, and biased graphs. These are graphs with additional structure that leads to new graphical matroids and other new kinds of graph theory, such as colorings and geometrical representations, of which ordinary graphical matroids, colorings, etc., are special cases. In combinatorial geometry I work on arrangements of hyperplanes and lattice-point counting. Other research interests are in graph theory and in generalizing Sperner's theorem.
Courses
Fall 2026
| Course |
Section |
Title |
Schedule |
Room |
| Math 507 |
01 |
Linear Algebra and Matrix Theory |
MWF 12:15–1:15
|
WH-100E
|
| Math 580A |
01 |
Topics in Combinatorial Analysis |
MWF 1:30–2:30
|
WH-309
|
Ph.D. Students
-
Michael Gottstein,
Spring, 2024
— Partitions and Gain Graphs
-
Nicholas Lacasse,
Spring, 2023
— Signed Graphs & Gain Graphs:Packing, Root Systems,Alcoves & Arrangements
-
Christopher Eppolito,
Summer, 2022
(Co-advisor:
Laura Anderson)
— Matroids: Mystic Monoliths, Meta Missiles, and Myopic Meadows
-
Amelia Mattern,
Spring, 2020
— Deficiency in Signed Graphs
-
Richard Behr,
Spring, 2018
— Edge Coloring and Special Edges of Signed Graphs
-
Simon Joyce,
Fall, 2017
— Interaction Graphs Derived From Activation Functions and Their Application to Gene Regulation
-
Alexander Schaefer,
Summer, 2017
— Permutable Matchings and Negative Cycle Vectors
-
Jackie Kaminski,
Summer, 2013
— Classification of Factored Gain-Graphic Hyperplane Arrangements
-
Nathan Reff,
Spring, 2012
— Gain Graphs, Group-Oriented Hypergraphs, and Matrices
-
Lucas Rusnak,
Spring, 2010
— Oriented Hypergraphs
-
Garry Bowlin,
Summer, 2009
— Maximum Frustration of Bipartite Signed Graphs
-
Garry Bowlin,
Summer, 2009
— Maximum Frustration of Bipartite Signed Graphs
-
Rigoberto Florez,
Summer, 2005
— Four Studies in the Geometry of Biased Graphs
-
Lori Koban,
Summer, 2004
— Two Generalizations of Biased Graph Theory: Circuit Signatures and Modular Triples of Matroids, and Biased Expansions of Biased Graphs
-
Steven Tedford,
Spring, 2002
— A Characterization of the Mixed Branching Greedoid
-
Daniel Slilaty,
Summer, 2000
— Orientations of Biased Graphs and Their Matroids
-
Steve Pagano,
Spring, 1998
— Separability and Representability of Bias Matroids of Signed Graphs
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