



Tropical and Nonarchimedean Geometry (edited with Omid Amini and Xander Faber), Contemporary Mathematics 605, American Mathematical Society, 2013.
Potential Theory and Dynamics on the Berkovich Projective Line, with Robert Rumely, AMS Mathematical Surveys and Monographs 159 (2010), 428 pages.
Descartes' rule of signs, Newton polygons, and polynomials over hyperfields, with Oliver Lorscheid, submitted.
Geometric bijections for regular matroids, zonotopes, and Ehrhart theory, with Spencer Backman and Chi Ho Yuen, submitted.
Matroids over partial hyperstructures, with Nathan Bowler, Advances in Mathematics 343 (2019), 821863.
The Bernardi process and torsor structures on spanning trees, with Yao Wang, International Mathematics Research Notices 16 (2018), 5120–5147.
Weight functions on Berkovich curves, with Johannes Nicaise, Algebra & Number Theory 10 (2016), 20532079.
Nonarchimedean geometry, tropicalization, and metrics on curves, with Sam Payne and Joe Rabinoff, Algebraic Geometry 3 no. 1 (2016), 63105.
Bitangents of tropical plane quartic curves, with Yoav Len, Ralph Morrison, Nathan Pflueger, and Qingchun Ren, Mathematische Zeitschrift 282 no. 3 (2016), 10171031.
Lifting harmonic morphisms II: Tropical curves and metrized complexes, with Omid Amini, Erwan Brugalle, and Joe Rabinoff, Algebra & Number Theory 9 no. 2 (2015), 267315.
Lifting harmonic morphisms I: Metrized complexes and Berkovich skeleta, with Omid Amini, Erwan Brugalle, and Joe Rabinoff, Research in the Mathematical Sciences 2 no. 7 (2015).
Linear series on metrized complexes of algebraic curves, with Omid Amini, Mathematische Annalen 362 no. 12 (2015), 55106.
The skeleton of the Jacobian, the Jacobian of the skeleton, and lifting meromorphic functions from tropical to algebraic curves, with Joseph Rabinoff, International Math. Research Notices 16 (2015), 74367472.
Canonical representatives for divisor classes on tropical curves and the MatrixTree Theorem, with Yang An, Greg Kuperberg, and Farbod Shokrieh, Forum of Mathematics, Sigma 2 (2014), e24, 25 pages.
On the structure of nonArchimedean analytic curves, with Joseph Rabinoff and Sam Payne, Contemporary Mathematics 605 (2013), 93121.
Special curves and postcriticallyfinite polynomials, with Laura DeMarco, Forum of Mathematics, Pi 1 (2013), e3, 35 pages.
Chip firing games, potential theory on graphs, and spanning trees, with Farbod Shokrieh, J. Combinatorial Theory Series A 120, no. 1 (2013), 164182.
Preperiodic points and unlikely intersections, with Laura DeMarco, Duke Math Journal 159, no. 1 (2011), 129.
Metric properties of the tropical AbelJacobi map, with Xander Faber, Journal of Algebraic Combinatorics 33, no. 3 (2011), 349381.
Harmonic morphisms and hyperelliptic graphs, with Serguei Norine, International Math. Research Notices 15 (2009), 29142955.
A finiteness theorem for canonical heights attached to rational maps over function fields, J. Reine Angew. Math 626 (2009), 205233.
Specialization of linear systems from curves to graphs, Algebra & Number Theory 2, no. 6 (2008), 613653.
A finiteness property of torsion points, with Suion Ih and Robert Rumely, Algebra & Number Theory 2, no. 2 (2008), 217248.
RiemannRoch and AbelJacobi theory on a finite graph, with Serguei Norine, Advances in Mathematics 215 (2007), 766788.
Harmonic analysis on metrized graphs, with Robert Rumely, Canad. J. Math. 59, no. 2 (2007), 225275.
A lower bound for average values of dynamical Green's functions, Mathematical Research Letters 13, no. 2 (2006), 245257.
Equidistribution of small points, tational dynamics, and potential theory, with Robert Rumely, Ann. Inst. Fourier (Grenoble) 56, no. 3 (2006), 625688.
Global discrepancy and small points on elliptic curves, with Clayton Petsche, International Math. Research Notices 61 (2005), 37913834.
Finiteness results for modular curves of genus at least 2, with Enrique GonzalezJimenez, Josep Gonzalez, and Bjorn Poonen, Amer. J. Math. 127, no. 6 (2005), 13251387.
Canonical heights, transfinite diameters, and polynomial dynamics, with LiangChung Hsia, J. Reine Angew. Math 585 (2005), 6192.
Equidistribution of small subvarieties of Abelian varieties, with Suion Ih, New York J. Math. 10 (2004), 279285.
A lower bound for the canonical height on Abelian varieties over Abelian extensions, with Joseph Silverman, Mathematical Research Letters 11 (2004), 377396.
Galois theory and torsion points on curves, with Ken Ribet, Les XXII^{èmes} Journées Arithmétiques (Lille, France), Journal de Théorie des Nombres de Bordeaux 15 (2003), 1132.
Lower bounds for the canonical height on elliptic curves over Abelian extensions, International Math. Research Notices 29 (2003), 15711589.
Automorphisms of X_{0}^{*}(p), with Yuji Hasegawa, Journal of Number Theory 100, no. 1 (2003), 7287.
Torsion packets on curves, with Bjorn Poonen, Compositio Math. 127 (2001), 109116.
Torsion points on modular curves, Inventiones Math. 140 (2000), 487509.
Cartier points on curves, International Math. Research Notices 7 (2000), 353370.
Kamienny's criterion and the method of Coleman and Chabauty, Proceedings of the A.M.S. 127, no. 10 (1999), 28512856.
Robert F. Coleman 19542014, with Barry Mazur and Ken Ribet, Research in the Mathematical Sciences 2 no. 1 (2015).
Degeneration of linear series from the tropical point of view and applications, with David Jensen, in Nonarchimedean and Tropical Geometry (edited with Sam Payne), Simons Symposia, SpringerVerlag, 2016.
An introduction to Berkovich analytic spaces and nonArchimedean potential theory on curves, padic Geometry (Lectures from the 2007 Arizona Winter School), AMS University Lecture Series, 2008.
Uncountable sets and an infinite real number game, Mathematics Magazine 80, no.5 (December 2007), 377380.
Metrized graphs, electrical networks, and Fourier analysis, with Xander Faber, Contemporary Mathematics 415, Proceedings of the Joint Summer Research Conference on Quantum Graphs and Their Applications, Snowbird, Utah, 2006.
Lecture notes for a graduate course in Algebraic Number Theory
Slides for my talk at the BP Centennial Conference in Cambridge, MA (pdf)
Slides for my talk at the Second ERC Research Period on Diophantine Geometry in Cetraro, Italy (pdf)
Slides for my talk at the Szpiro Birthday Conference at the CUNY Graduate Center (pdf)
Slides for my talk at the 2009 Journées Arithmétiques in St. Etienne, France (pdf)
Slides for my talk at the MSRI conference "Modular Forms and Arithmetic" (pdf)
Slides for my talks at the Arizona Winter School (March 2007): Lecture 1, 2, 3, 4, 5
Slides for my talks at the MSRI Introductory Workshop on Rational Points : Lecture 1, 2
Zolotarev's magical proof of the Law of Quadratic Reciprocity
Uniform structures and Berkovich spaces
The Prime Number Theorem, with Dennis Clark