Interests: 
My interests are algebraic combinatorics (KazhdanLusztig polynomials, combinatorics of Weyl groups, and diagonal harmonics) and gerrymandering

CV: 
PDF format

Gerrymandering. 
 Interactions between geographic clustering and district size
In preparation.
 Gerrymandering and the net number of US House seats won due to votedistribution asymmetries (also on arXiv)
Joint with J. Buzas.
Ver. 2 (minor revisions)
Submitted.
Guest post on Rick Hasen's Election Law Blog.
 Quantifying gerrymandering using the vote distribution (also on arXiv)
To appear, Election Law Journal
gzipped tar file of python code used to generate data in ELJ paper
Friendly introduction to the declination introduced in above article.
The declination is essentially the angle between the two black lines.
The bigger the angle, the more partisan asymmetry. Click below to enlarge.
Python code to compute the declination.
Click the image for animation from 1972 to 2016
Notes on the animation:
 The cartogram adjusts state sizes according to the
number of congressional seats.
The sizes used are based on the sizes of the 2012
congressional declinations.
 The version of the declination used is one (delta
tilde) that is essentially independent of the number of
seats.
The 2003 Texas redistricting is striking.
 States without at least one seat won by each party are in gray.
 Sorry Don Young and HI, you didn't fit.

Combinatorics. 
 Quasisymmetric and Schur expansions of cycle index polynomials
Joint with N. Loehr.
Submitted.
Sage worksheet for computations in the paper. also as a text file
 Orthogonal bases for transportation polytopes applied to Latin squares, magic squares and Sudoku boards
In revision.
Sage worksheet for constructing bases described in the paper.
 Combinatorics of the mirabolic RSK correspondence
Joint with J. Godbout
Eternally in preparation.
 Motzkin identities arising in the computation of modified Macdonal polynomials
Joint with D. Velleman
Eternally in preparation.
 Sweep maps: A continuous family of sorting algorithms
Joint with D. Armstrong and N. Loehr
Sage worksheet for checking various conjectures described in the paper.
Advances in Mathematics, 284 (2015), 15985.

Rational parking functions and Catalan numbers
Joint with D. Armstrong and N. Loehr
Sage worksheet for checking various conjectures described in the paper.
To appear, Annals of Combinatorics.

Shape and pattern containment of separable permutations
Joint with A. Crites and G. Panova
Ars Combinatoria, to appear.
 Martin Gardner's minimum nothreeinaline problem
Joint with A. Cooper, O. Pikhurko and J. Schmitt
American Mathematical Monthly, 121:3 (2014), 213221.
 Transition matrices for symmetric and quasisymmetric HallLittlewood polynomials
Joint with N. Loehr and L. Serrano
Journal of Combinatorial Theory, Series A, 120:8 (2013), 19962019.
Sage worksheet for computing various matrices described in the paper.
 On the existence of three dimensional Room frames and Howell cubes
Joint with J. Dinitz and E. Lamken
Discrete Math, 313:12 (2013), 13681384. Find it here.
 What to expect from a game of Memory
Joint with D. Velleman
American Mathematical Monthly, 120:9 (2013), 787805.

Quasisymmetric expansions of Schurfunction plethysms
Joint with N. Loehr
Proceedings of the AMS, 140 (2012), 11591171.
 Equivalence classes for the mucoefficient of KazhdanLusztig polynomials in S_n
Experimental Math., 20 (2011), no. 4, 457466.
 The Spectra of Certain Classes of Room Frames: The Last Cases
Joint with J. Dinitz
Elec. J. Combin. 17 (2010), no. 1, Research Paper 74, 13 pp.
 From quasisymmetric expansions to Schur expansions via a modified inverse Kostka matrix
Joint with E. Egge and N. Loehr
European J. Combin. 31 (2010), no. 8, 20142027.
 A combinatorial version of Sylvester's fourpoint problem
Adv. in App. Math., 45 (2010) no. 3, 390394.
 A continuous family of partition statistics equidistributed
with length
Joint with N. Loehr
J. Combin. Theory Ser. A 116 (2009), no. 2, 379403.
(final version)

Nested quantum Dyck paths and nabla(s_lambda)
Joint with N. Loehr
International Mathematics Research Notices 2008; Vol 2008: article ID rnm157 (final version)

Bitableaux bases for GarsiaHaiman modules of hollow type
Joint with E. Allen and M. Cox
J. Combin. Theory Ser. A 115 (2008), no. 7, 11271155.

A human proof for a generalization of Shalosh B. Ekhad's 10^n Lattice Paths Theorem
Joint with N. Loehr and B. Sagan
Ars Combin. 89 (2008), 421429.
 Square q,tlattice paths and nabla(p_n)
Joint with N. Loehr
Transactions of the AMS, 359 (2007) no. 2, 649669.
 The combinatorics of a threeline
circulant determinant
Joint with N. Loehr and H. Wilf
Israel Journal of Mathematics 143 (2004), 141156
 Juggling probabilities
American Mathematical Monthly 112, no. 2 (2005), 105118

Counterexamples to the 0,1Conjecture
Joint with T. McLarnan
Represent. Theory 7 (2003), 181195
(final version)

A formula for inverse KazhdanLusztig polynomials in S_n.
J. Comb. Theory A, Vol. 104, Iss. 2 , November (2003), 301316
(final version)

Maximal singular loci for Schubert varieties in SL(n)/B.
Joint with S. Billey
Trans. AMS 355 (2003), no. 10, 39153945 (electronic)
(final version)

KazhdanLusztig polynomials for
321hexagonavoiding permuations.
Joint with S. Billey
J. of Alg. Comb., 13 (2): 111136, March 2001
(final version)

Misc.: 
 TBA
Joint with Jill Warrington
In preparation.
 TBA
Michelle L. Brown, Therese M. Donovan, Ruth M. Mickey, Gregory S. Warrington, W. Scott Schwenk, David M. Theobald
In revision.
 Estimating landscape carrying capacity through
maximum clique analysis
Joint with Therese M. Donovan, W. Scott Schwenk and Jeffrey H. Dinitz
Ecological Applications, 22:8 (2012), 22652276.
 A Photographic Assignment for Abstract Algebra
PRIMUS 19 (2009), no. 6, 561564.

Not refereed: 
 The shape of a pool.
Eternally in preparation.
 Juggling Performers + Math = ?
Math Horizons, Feb. 2008.
 Randomized voting and
A sketch of randomized voting.
In limbo.

Talks: 
Here are the overheads for some of the talks I have given:
 Quasisymmetric expansions of cycle indices
UGA AMS Sectional Meeting; Mar. 2016
 Rational Catalan numbers and the sweep map
UVMSt. Michael's Combinatorics Seminar; Nov. 2014
 Rational qCatalan numbers and qbinomials
Halifax AMS Sectional Meeting; Oct. 2014
 The Sweep Map
CMS Winter Meeting  Ottawa; Dec. 2013
 Quasisymmetric expansions of Schur plethysms
Holy Cross AMS Sectional Meeting; Apr. 2011
 On the mucoefficient of KazhdanLusztig polynomials
Holy Cross AMS Sectional Meeting; Apr. 2011
 An infinite family of partition statistics
Penn State AMS Sectional Meeting; Oct. 2009
 "Statistics" in Combinatorics
Invited talk, MathFest Aug. 2009 in Portland, OR
 A variation on Sylvester's fourpoint problem
Gems of Combinatorics Session, MathFest Aug. 2009 in Portland, OR
 Combinatorial structures associated to the nabla operator
Banff, Sep. 2007 (Jim Haglund, proxy speaker; thanks Jim!)
 Combinatorial aspects of nabla(s_lambda)
given at CRM, Montreal in May 2007.
 Square q,tlattice paths and nabla(p_n)
given at FPSAC '05 in Taormina, Sicily in June 2005.
 Overview of KazhdanLusztig Polynomials
given at UPenn combinatorics seminar in October 2003.
 Counterexamples to the
0,1Conjecture
given at the Computational Lie Theory conference at
CRM in June 2002.
 Maximal Singular Loci for Schubert Varieties in SL(n)/B
given at FPSAC '01 meeting in Scottsdale, AZ in May 2001.
 KazhdanLusztig
polynomials for 321hexagonavoiding permutations
given at the Joint Meeting in Washington, DC in January 2000.

Thesis: 
Here is my doctoral thesis.
My thesis advisor was
Sara Billey
at MIT (now at Univ. Washington). You can check out my mathematical genealogy
at The Mathematics Genealogy Project.

Code: 
 My cyborg juggling balls.
 Code for computing typeA KazhdanLusztig polynomials.
This is the code accompanying my paper Equivalence classes for the mucoefficient
of KazhdanLusztig polynomials in S_n.
 Some old code for computing typeA KazhdanLusztig polynomials.

Trajectory: 
From F01 to S03 I was a postdoc at the University of Massachusetts at
Amherst. From F03 to S04 I was an NSF postdoctoral fellow at the
University of Pennsylvania. From F04 to F08 I was
an Assistant Professor at
Wake Forest University in WinstonSalem, NC.
From S09 to S14 I was an Assistant Professor at
the University of
Vermont in Burlington, VT.
In S14 I was promoted to
Associate Professor with tenure (effective F14).
