I am an Assistant Professer at UofL. Most recently, I was a postdoc at UCSD working with Fan Chung on various aspects of random graphs and spectral graph theory. Recently we have uncovered some exciting and surprising properties of selfish routing in networks, showing that in a wide variety of situations removing connections can improve the behavior of the network. Ironically, the heart of this result is the observation that the properties of the network which facilitate excellent performance for non-selfish routing are the same properties that allow the selfish routing to reduce the network performance.
Before going to UCSD, I received my Ph.D. in 2008 from Georgia Tech through the Algorithms, Combinatorics and Optimization program. The ACO program is an interdisciplinary program sponsored by the College of Computing, H. Milton Stewart School of Industrial and Systems Engineering and the School of Mathematics focusing on the interaction and boundary between these fields. While at Georgia Tech I was mentored/advised by Milena Mihail and Tom Trotter. My thesis work with my adviser, Milena Mihail, focused on developing a model for complex networks such as the internet that incorporated semantic information. In my work with Tom Trotter and his graduate students, I focused on the combinatorial structure of partially ordered sets. Perhaps the most widely known result stemming from this collaboration concerns the existence of a specialized partition of the subset lattice which has important application to a long standing conjecture in commutative algebra.
While at University of Louisville, UCSD, and Georgia Tech I have been lead instructor for thirteen classes, teaching introductory material in both mathematics and computer science. I have experience teaching both large lecture classes and smaller more intimate classes and understand the challenges that come with each. This semester I am teaching Discrete Mathematics and Mathematics for Elementary Education II. I am also teaching an informal course on spectral graph theory this semester.