Justin Troyka Visiting Assistant Professor of Mathematics and Computer Science
- Ph.D. Dartmouth College
- B.A. Carleton College
Areas of Expertise
I am a Visiting Assistant Professor in mathematics, researching enumerative and algebraic combinatorics. After earning my Ph.D. at Dartmouth with advisor Sergi Elizalde, I worked in a postdoctoral position for two years at York University, in Toronto, where I researched permutation patterns with Neal Madras. I'm excited to be here at Davidson for two years and teach fun and interesting classes!
In my research, I like to count things such as permutations, partitions, and graphs, often with the help of symmetric functions and other algebraic objects. My favorite questions in this area are asymptotic: for instance, I have proved results about how many "very large" cyclic permutations have a given descent set, and I have proved a conjecture on the number of "very large" split graphs—in both cases, "very large" means we are taking the limit as the size of the structure is going to infinity. In much of this work I have applied analysis and probability to answer questions about combinatorics.
If you're a student in one of my classes, don't hesitate to email me if you have any questions—I look forward to meeting you!