I am a Professor of Mathematics here at Penn.
I am co-organizer
Elizabeth Beazley of Haverford College,
Linda Chen of Swarthmore College,
Jennifer Morse of Drexel University, and
Mark Skandera of Lehigh University) of the
Philadelphia CAGE (Combinatorics and Algebraic Geometry)
seminar (Certain Tuesdays and Thursdays afternoons from 2 to 3pm in DRL 4C2).
Last years CAGE seminar
My research interests are in algebraic and enumerative
In particular, I work on problems involving symmetric functions and Macdonald polynomials,
combinatorial statistics and q-analogs,
rook polynomials, and am also interested in the zeros of polynomials and analytic functions.
I like experimental mathematics, and
often use computer algebra packages such as Maple in my research, to develop
and test conjectures.
Publications and Preprints,
The q,t-Catalan Numbers and the Space of Diagonal Harmonics
in pdf format
or ps format
The official bound version of this book can be ordered from the AMS. It is part of the
AMS University Lecture Series.
Math 432 (Game Theory)
Transparencies from Selected Presentations
The (q,t)-Catalan Numbers and the Space of
Diagonal Harmonics, hour long Invited Address, AMS Sectional, Orlando Fl. Nov. 9, 2002.
A Combinatorial Model for the Macdonald Polynomials
(in pdf format), or postscript format, hour long
presentation at the
Workshop on Resolutions, Inverse Systems, and Coinvariants, University of Ottawa, Jan. 13, 2005.
Recent Combinatorial Results involving
Macdonald Polynomials and Diagonal Harmonics
(in postscript format), or
at the 18th International Conference on Formal Power Series and Algebraic Combinatorics
(FPSAC '06), San Diego, CA, June 22, 2006.
The Monotone Column Permanent Conjecture and Multivariate Eulerian Polynomials
, hour long
presentation at the 26th
Clemson mini-Conference on Discrete Mathematics and Algorithms, Clemson University, Oct. 28, 2011.
The PhD Oral Exam in Combinatorics at Penn
PhD and Masters Students
Some Past Workshops
BIRS Workshop on Applications of Macdonald Polynomials, September 9-14, 2007
Oberwolfach Workshop on Combinatorial Representation Theory, March 22-27, 2010
BIRS Workshop on Quasisymmetric Functions, November 14-19, 2010
Upcoming Presentations and Conferences
MAA Invited paper Session on Where Have All the Zeros Gone?, joint meetings of the AMS and MAA, San Diego, Jan 9-12, 2013
AMS Special Session on Combinatorial Avenues in Representation Theory, Univ. of Colorado, Boulder, CO, April 13-14, 2013
I will be giving two talks on Macdonald Polynomials and also a number theory seminar
Korea Institute for Advanced Study (KIAS) in Seoul, Korea, during the week of May 13-17, 2013
FPSAC 2013, Paris, France, June 24-28, 2013
MFO Workshop on Enumerative Combinatorics, Oberwolfach, Germany, March 2-8, 2014
Proceedings of the American Mathematical Society
Journal of Combinatorics
Bulletin of Parana's Mathematical Society
Member of the AMS and MAA
Fellow of the AMS
Department of Mathematics
ADDRESS>University of Pennsylvania
209 South 33rd St.
David Rittenhouse Laboratory
Philadelphia, PA 19104-6395