Rate My Professor Wesley Hough

Wesley K. Hough, Ph.D., serves as an Associate Professor of Mathematics at the University of Wisconsin-Whitewater. His primary research interests are in topological combinatorics, focusing on the application of discrete Morse theory to detect properties of topological spaces generated by combinatorial structures. These include connectivity bounds, Euler characteristics, dimensions of non-vanishing homology, and cellular counting recursions. Introduced to discrete Morse theory during a Research Experience for Undergraduates at James Madison University in summer 2011, his early work examined the poset topology of pattern-avoiding permutation groups under the strong Bruhat order. Recent investigations cover homomorphism complexes arising from mapping chain posets into Boolean algebras and more general distributive lattices, as well as matching trees and the independence and matching complexes of small grid graphs.

Hough earned his Ph.D. in Mathematics from the University of Kentucky in May 2017, with dissertation titled 'On Independence, Matching, and Homomorphism Complexes' under advisor Benjamin Braun. He received his M.A. in Mathematics from the University of Kentucky in August 2014 and a B.A. with double majors in mathematics and economics from Hanover College in May 2012. His selected publications include 'Homomorphism complexes and maximal chains in graded posets' (with B. Braun, European Journal of Combinatorics 80:178-194, 2019), 'Matching and independence complexes related to small grids' (with B. Braun, Electronic Journal of Combinatorics 24(4):P4.18, 2017), and 'Permutation pattern avoidance and the Catalan triangle' (with D. DeSantis, R. Field, B. Jones, R. Meissen, and J. Ziefle, Missouri Journal of Mathematical Sciences 25(1):50-60, 2013). At UW-Whitewater, he teaches courses such as Graph Theory, Discrete Mathematics, Mathematical Statistics, Applied Probability Theory, and Quantitative Reasoning. Hough contributes to university service through curriculum development and management, transfer credit evaluation as Transfer Review Coordinator, and leadership in the Mathematical Association of America Wisconsin Section as Chair-Elect and former Project NExT Director. During graduate studies, he received a UKAEF Fellowship.