39. Intersection matrices of wild cyclic quotient singularities, Preprint 2024. Compendium of known small intersection matrices. 38. Torsion and exceptional units, To appear in Acta Arith. Data for number fields of degree 8 to 12. 37. The critical polynomial of a graph, J. Number Theory 257 (2024), 215–248. 36. With S. Schroeer, Discriminant groups of wild cyclic quotient singularities, Algebra Number Theory 17 (2023), no. 5, 1017–1068. 35. With M. Melistas, A. Suresh, M. Suwama, and H. Wang, Integer dynamics, Int. J. Number Th. 18 (2022), no. 02, 397–415. 34. With S. Schroeer, Moderately ramified actions in positive characteristic, Math. Zeit. 295 (2020), 1095–1142. 33. With Q. Liu, New points on curves, Acta Arithmetica 186 (2018), no. 2, 101–141. Some remarks and computations related to the paper New points on curves. 32. With Q. Liu and M. 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Elementary Divisor domains and Bézout domains, J. of Algebra 371 (2012), 609-619. 24. Two-variable zeta-functions on graphs and Riemann-Roch theorems, Int. Math. Res. Notices, Volume 2012 Issue 22 (2012), 5100-5131. 23. Torsion and Tamagawa numbers, Ann. Inst. Fourier, 61 no. 5 (2011), 1995-2037. A question in elementary number theory related to 2.15 in [23]. 22. Models of curves and wild ramification, Pure Appl. Math. Q. 6 (2010), no. 1, Special Issue: In honor of John Tate, Part 2, 41-82. (Here are some updated references for the paper.) 21. Smith normal form and Laplacians, J. Combin. Theory B 98 (2008), 1271-1300. 20. Grothendieck's pairing for Jacobians and base change, J. Number Theory 128 (2008), 1448-1457. 19. With Q. Liu and M. Raynaud, On the Brauer group of a surface, Invent. math. 159 (2005), 673-676. A complement to an assertion in this paper. A corrigendum for [18] and [19] is found in [32]. 18. With Q. Liu and M. Raynaud, Néron models, Lie algebras, and reduction of curves of genus one, Invent. math. 157 (2004), 455-518. A complement to an assertion in this paper. 17. with S. Bosch, Grothendieck's pairing on component groups of jacobians, Invent. math. 148 (2002), 353-396. 16. with T. Tucker, Thue equations and the method of Chabauty-Coleman, Invent. math. 148 (2002), 47-77. 15. with Q. Liu, Special fibers of Néron models and wild ramification, J. reine angew. Math. 532 (2001), 179-222. A complement to Proposition 1.8 in this paper. 14. Reduction of points in the Néron model of a jacobian, J. reine angew. Math. 527 (2000), 117-149. 13. The arithmetic of the laplacian of a graph, LAMA 47 (2000), 281-306. 12. with Q. Liu, Models of curves and finite covers, Comp. Math. 118 (1999), 61-102. 11. with B. Edixhoven and Q. Liu, The p-part of the group of components of a Néron model, J. of Alg. Geom. 5 (1996), 801-813. 10. Torsion points on the modular jacobian J_0(N), Comp. Math. 96 (1995), 149-172. 9. On the group of components of a Néron model, J. reine angew. Math. 445, 109-160 (1993). 8. On modular elliptic curves, J. of Number Theory 44 (1993), 255-259. 7. Reducibility of polynomials in two variables, J. of Algebra 156 (1993), 65-75. 6. The characteristic polynomial of a monodromy transformation attached to a family of curves, Comm. Math. Helv. 68 (1993), 111-137. 5. Jacobians with potentially good ell-reduction, J. reine angew. Math. 430 (1992), 151-177. 4. On a finite group associated to the Laplacian of a graph, Discr. Math. 91 (1991), 277-282. 3. Dual graphs of degenerating curves, Math. Ann. 287 (1990), 135-150. 2. Groups of components of Néron models of jacobians, Comp. Math. 73 (1990), 145-160. 1. Arithmetical graphs, Math. Ann. 285 (1989), 481-501 Unpublished Manuscripts 5. With Z. Xiang, Integral points on variable separated curves. 2019. 4. With O. Gabber and Q. Liu, Period, Index, and an invariant of Grothendieck, 2010.3. Towers of curves and rational distance sets, 2005.2. Reduction in the case of imperfect residue fields , 2001.1. On the jacobian of the modular curve X_0(N), 1996. Book Reviews 3. Digital Dice: Computational Solutions to Practical Probability Problems, by Paul J. Nahin, Princeton University Press, 2008, published in the Mathematical Intelligencer, 32, number 1, 2010.2. Fearless Symmetry: Exposing the Hidden Patterns of Numbers, by Avner Ash and Robert Gross, Princeton University Press, 2006, published in the Notices of the American Math. Society, vol. 51, 2007.1. Diophantine Geometry: an Introduction, by Marc Hindry and Joseph H. Silverman, Graduate Texts in Mathematics, 201, Springer-Verlag, New York, 2000, published as a Featured Review in Math. Reviews, 2001. Some Talks 1. Avoidance Lemma in families and a Moving Lemma, Zürich conference, September 2012.2. The index of an algebraic variety, Hawaii conference, March 2012. Unpublished Dissertations of Former Students René-Michel Shumbusho, Elliptic curves with prime conductor and a conjecture of Cremona, 2004. Undergraduate Publications 1. Fall 2008 Undergraduate Research Seminar, sponsored by the department NSF VIGRE grant, On a generalization of the Frobenius number, Journal of Integer Sequences, Vol. 13 (2010).
