One really nice and unusual use of representation theory is in computing time to uniformity in group walks, as kindly explained to me by my postdoc mentor, Persi Diaconis; we worked on a classical random walk on the Heisenberg group using this Fourier Analytic approach and this explains several recent papers with a less obviously combinatorial bent.

- Applying Representation Theory to Random Walks. CAGE Seminar at U Penn. September, 2016
- A Random Walk on the Heisenberg Group. U.C. Davis Combinatorics Seminar. May, 2016
- Combinatorial
Challenges:
Formidable symmetries from the $q, t$ Catalan and Beyond. MAA Golden
Section Invited Speaker, Foothill University, February 2015.

- A simpler
formula for the number
of diagonal inversions of an ((m,n))-Parking Functions. AMS Special
Session, Dalhousie University, October 2014.

- Parallelogram
Polyominoes and
(Surprise!)-- The Diagonal Harmonics} York University, March 2014.

- The Diagonal
Harmonics and $n$
Capricious Wives} University of San Francisco Mathematics Colloquium
March 2014.

- Diagonal
Harmonics, Parking
Functions, and Parking Polynomials} Bay Area Discrete Math Day October
2013.

- Parallelogram Polyominoes, the Diagonal Harmonics, and a Surprising (!) Connection} UC Berkeley Combinatorics Seminar October 2013.
- Connections between a family of recursive polynomials and parking function theory, International Conference on Formal Power Series and Algebraic Combinatorics, Nagoya, Japan, August 2012.
- New Approaches to the Study of Parking Functions and the Theory of the Diagonal Harmonics, University of Washington Combinatorics Seminar, May 2012.
- A Family of Polynomials Suggested by the Haglund- Morse-Zabrocki Conjecture, Workshop de Algebra V Teoria de Numeros, Chile, December 2011.
- A New Parking Function Statistic, Special Session on Symmetric Functions, Symmetric Group Characters, and Their Generalizations, AMS Sectional Meeting, Wake Forest University, September 2011.
- A Parking Function Bijection Suggested by the Haglund-Morse-Zabrocki Conjecture, Banff International Research Institute for Mathematical Innovation and Discovery, November 2010.
- Two Parking Function Bijections, Universite de Bordeaux, France, December 2009.
- Combinatorics of the Diagonal Harmonics, MIT Women in Mathematics Lecture Series, March 2009.
- The Metric Dimension of the Cayley Digraphs of Finite Abelian Groups, AMS Session on Combinatorics, Joint Meetings, January 2007.
- Applications of Lie Symmetry Groups to Minimal Surfaces, Pi Mu Epsilon Session, MAA Mathfest, August 2005.