Angela Hicks

Research:

My primary research interest lies in the areas of algebraic combinatorics, representation theory, and symmetric function theory, and in particular symmetric and quasisymmetric functions.  As a more specific indication of my interests, I currently am actively thinking about particular problems related to: Macdonald polynomials and the n! conjecture, k-schur functions, rational Catalan combinatorics, random generation of combinatorial objects, and the sand pile model.  My doctoral thesis, completed under Adriano Garsia, concentrated on parking functions and their conjectured (proven?--see the latest exciting reasearch by Carlsson and Mellit) relation to the diagonal harmonics.

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.

Papers:

Selected Talks:

• 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.