Publications (Annotated list with abstracts available here):
Involutions on standard Young tableaux and divisors on metric graphs with
Rohit Agrawal, Vladimir Sotirov, and Fan Wei
Bases for cluster algebras from surfaces with Ralf Schiffler and Lauren Williams (To appear in Compos. Math.)
Matrix Formulae and skein relations for cluster algebras from surfaces with Lauren Williams (To appear in IMRN)
The Cyclotomic polynomial topologically with Vic Reiner (To appear in Journal für die reine und angewandte)
Linear Systems on Tropical Curves with Christian Haase and Josephine Yu
Math. Zeitschrift, Volume 270, 3-4 (2012), 1111-1140.
Also on the Arxiv.
A Compendium on the Cluster Algebra and Quiver Package in SAGE with Christian Stump,
Seminaire Lotharingien de Combinatoire 65 (2011), Article B65d
Positivity for cluster algebras from surfaces with Ralf Schiffler and Lauren Williams
Advances in Mathematics, Vol. 227, Issue 6 (2011), 2241--2308.
Also on the Arxiv.
A Graph Theoretic Expansion Formula for Cluster Algebras of Classical Type
Annals of Combinatorics, Volume 15, Number 1 (2011) 147--184
Also on the Arxiv, and presented at FPSAC 2008.
Cluster expansion formulas and perfect matchings with Ralf Schiffler
Journal of Algebraic Combinatorics, Vol. 32, Number 2 (2010), 187--209
Also on the Arxiv.
The critical groups of a family of graphs and elliptic curves over finite fields. Journal of Algebraic Combinatorics: Vol. 30, Issue 2 (2009), 255--276
Preprint also presented at FPSAC '07 at Tianjin, China.
Invariants, Kronecker Products
and Combinatorics of some Remarkable Diophantine systems (Extended Version)
with Adriano Garsia, Nolan Wallach, and Guoce Xin.
Adv. in Appl. Math. 42 (2009), no. 3, 392--421
A new characterization for the m-quasiinvariants
of S_n and explicit basis for two row hook shapes
with Jason Bandlow. J. Combin. Theory Ser. A, 115 (2008), no 8, 1333-1357 Also presented at FPSAC 2008.
Combinatorial Aspects of Elliptic Curves
Seminaire Lotharingien de Combinatoire 56 (2007), Article B56f
Also presented at FPSAC '06 at San Diego.
Combinatorial Interpretations for Rank-Two Cluster Algebras of Affine Type
with Jim Propp
Electronic Journal of Combinatorics. Vol. 14 (R15), 2007.
Quasiinvariants of S_3 with Jason Bandlow.
J. Combin. Theory Ser. A 109 (2005), no 2, 281-298
Slides from selected Talks:
Brane Tilings and Cluster Algebras: Joint Meetings of the AMS and MAA at San Diego, January 11, 2013 (Versions also given at
UC Berkeley, MSRI, and the 2012 Canadian Summer Math Meeting)
Bases for Cluster Algebras from Surfaces: Bay Area Discrete Math Day, November 17, 2012 (Also given at
UC Davis, University of Toronto, University of Minnesota, BIRS, ICERM)
A Topological Interpretation of the Cyclotomic Polynomial, FPSAC, June 16, 2011 (Also given at MIT, University of Minnesota, and UQAM)
Linear Systems on Tropical Curves, Combinatexas, April 16, 2011 (Also given at FPSAC 2010, SIAM DM10, the 2010 Canadian Summer Math Meeting, UCSD, and UC Berkeley)
Elliptic Curves and Chip-Firing Games on Graphs: University of Minnesota, Dec. 3, 2009
(Also given at UC Berkeley, University of Kentucky, UCSD, Dartmouth, UC Davis, MIT, University of Kansas, Tulane University, Georgia Tech, and San Francisco State University, Stanford University, Arizona State University, MSRI, and USC)
Cluster Algebras of Triangulated Surfaces and Snake Graphs: Brown University, Feb. 9, 2010
(Also given at University of Michigan, at the
Maurice Auslander Distinguished Lectures and International Conference, at UQAM, MIT, University of Washington, Texas A&M, University of Minnesota, Ohio State University, and University of Pittsburgh.
Abridged versions given at FPSAC 2009, the AMS Fall 2009 Eastern Sectional at Penn State, and MSRI.)
Graph Theoretical Cluster Expansion Formulas: International Conference on Cluster Algebras and Related Topics - Mexico City - December 19, 2008
A Graph Theoretic Interpretation for Cluster Algebras of Classical Type: Northeastern University - Representation Theory Seminar - March 14, 2008
(Also given at UMass Amherst, University of Pennsylvania, and MIT)
The Zeta Function of a Cyclic Language with Connections to Elliptic Curves and Chip-Firing Games: Recent Progress in Combinatorics on Words - CRM - March 14, 2007 (Similar talks given at FPSAC 2006, UQAM, and UCSD)
The m-Quasiinvariants of S_n: Joint Meetings of the AMS and MAA at Phoenix - January 9, 2004
Theses and other Documents:
My Ph.D. Thesis- A Combinatorial Comparison of Elliptic Curves and Critical Groups of Graphs
My undergraduate thesis - Cluster Algebras, Somos Sequences, and Exchange Graphs.
Combinatorial Interpretations for the Markoff Numbers (Unpublished preprint) with Andy Itsara, Jim Propp, and Rui Viana, as part of the REACH program
Schoof's Algorithm for Counting Points on E(F_q)
(Math 168 Project under direction of William Stein)