Matt Baker's Papers

Research papers

Specialization of Linear Systems from Curves to Graphs, submitted.

Harmonic Morphisms and Hyperelliptic Graphs, with Serguei Norine, submitted.

A Finiteness Property of Torsion Points, with Su-ion Ih and Robert Rumely, to appear in Algebra and Number Theory.

A Finiteness Theorem for Canonical Heights Attached to Rational Maps over Function Fields, to appear in J. Reine Angew. Math.

Riemann-Roch and Abel-Jacobi Theory on a Finite Graph, with Serguei Norine, Advances in Mathematics 215 (2007), 766--788.

Harmonic Analysis on Metrized Graphs, with Robert Rumely, Canad. J. Math. 59, no. 2 (2007), 225--275.

A Lower Bound for Average Values of Dynamical Green's Functions, Mathematical Research Letters 13, no. 2 (2006), 245--257.

Equidistribution of Small Points, Rational Dynamics, and Potential Theory, with Robert Rumely, Ann. Inst. Fourier (Grenoble) 56, no. 3 (2006), 625--688.

Global Discrepancy and Small Points on Elliptic Curves, with Clayton Petsche, International Math. Research Notices 61 (2005), 3791--3834.

Finiteness Results for Modular Curves of Genus at least 2, with Enrique Gonzalez-Jimenez, Josep Gonzalez, and Bjorn Poonen, Amer. J. Math. 127, no. 6 (2005), 1325--1387.

Canonical Heights, Transfinite Diameters, and Polynomial Dynamics, with Liang-Chung Hsia, J. Reine Angew. Math 585 (2005), 61--92.

Equidistribution of Small Subvarieties of Abelian Varieties, with Su-ion Ih, New York J. Math. 10 (2004), 279-285.

A Lower Bound for the Canonical Height on Abelian Varieties over Abelian Extensions, with Joseph Silverman, Mathematical Research Letters 11 (2004), 377-396.

Galois Theory and Torsion Points on Curves, with Ken Ribet, Les XXIIèmes Journées Arithmétiques (Lille, France), Journal de Théorie des Nombres de Bordeaux 15 (2003), 11-32.

Lower Bounds for the Canonical Height on Elliptic Curves over Abelian Extensions, International Math. Research Notices 29 (2003), 1571-1589.

Automorphisms of X0*(p), with Yuji Hasegawa, Journal of Number Theory 100, no. 1 (2003), 72-87.

Torsion Packets on Curves, with Bjorn Poonen, Compositio Math. 127 (2001), 109-116.

Torsion Points on Modular Curves, Inventiones Math. 140 (2000), 487-509.

Cartier Points on Curves, International Math. Research Notices 7 (2000), 353-370.

Kamienny's Criterion and the Method of Coleman and Chabauty, Proceedings of the A.M.S. 127, no. 10 (1999), 2851-2856.

Research monographs

Potential Theory on the Berkovich Projective Line, with Robert Rumely, in preparation.

Ph.D. Thesis

Torsion Points on Modular Curves, Doctoral dissertation, UC Berkeley (1999), written under the supervision of Robert Coleman.

Fun papers

Uncountable Sets and an Infinite Real Number Game, Mathematics Magazine 80, no.5 (December 2007), 377-380.

Metrized Graphs, Laplacian Operators, and Electrical Networks, with Xander Faber, Contemporary Mathematics 415, Proceedings of the Joint Summer Research Conference on Quantum Graphs and Their Applications, Snowbird, Utah, 2006.

Lecture notes

My 2007 Arizona Winter School Lecture Notes entitled "An Introduction to Berkovich Analytic Spaces and Non-Archimedean Potential Theory on Curves" (last revision 12/17/07)

Course notes

Algebraic Number Theory (revised December 2006)

Student papers

Carmichael Numbers in Number Rings by my undergraduate REU student Ander Steele, to appear in the Journal of Number Theory.

Expository papers

The Prime Number Theorem, with Dennis Clark

Other

Uniform Structures and Berkovich Spaces, preprint.

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This page was last modified on January 29, 2008 by Matt Baker.