Professor of Mathematics
University of Pennsylvania
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 Area Combinatorics and Algebraic Geometry (CAGE) Seminar
seminar (Tuesdays from 2:30-3:30pm in Korman Center 245 at Drexel and/or
Thursdays from 2:30-3:30pm in the DRL MPA Library seminar room at Penn).
CAGE Fall 2013
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 299 (Undergraduate Math Research)
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
Special Session on Geometric Applications of Algebraic Combinatorics, January 17-18, 2014, Joint Math Meetings, Baltimore, Maryland.
MIT Combinatorics Seminar, Feb. 7, 2014, 4:15-5:15pm.
UCLA Combinatorics Seminar, Feb. 13, 2014
MFO Workshop on Enumerative Combinatorics, Oberwolfach, Germany, March 2-8, 2014
BruceFest: Conference on Bijective and Algebraic Combinatorics in honor of Bruce Sagan's 60th birthday, University of Florida, Gainesville, March 24-25, 2014
IMA Workshop on Geometric and Enumerative Combinatorics, University of Minnesota, Minneapolis, November 10-14, 2014
Conference in honor of Michelle Wachs, Miami, Florida, January 6-9, 2015.
Journal of Combinatorics
Bulletin of Parana's Mathematical Society
Member of the AMS and MAA
Fellow of the AMS
Department of Mathematics
University of Pennsylvania
209 South 33rd St.
David Rittenhouse Laboratory
Philadelphia, PA 19104-6395