John Voight

Assistant Professor of Mathematics and Computer Science
Department of Mathematics and Statistics
Department of Computer Science
College of Engineering and Mathematical Sciences
University of Vermont

Address:
Department of Mathematics and Statistics
16 Colchester Ave
University of Vermont
Burlington, VT 05401
USA

Office: 16 Colchester Ave, 207C
Email: jvoight@gmail.com
Phone: (802) 656-2271
Homepage: http://www.cems.uvm.edu/~jvoight/
Office hours (Spring 2013): By appointment!

Research Interests:

L-Functions and Modular Forms Database (LFMDB)

Algorithms for lattices and algebraic automorphic forms (AIM)

Courses:

Past Courses (UVM):

Past Courses (Berkeley):

Curriculum Vitae:

Publications:

Please note that the versions that appear here may differ from the published version, as some errata have been corrected. The version here is the most updated; the arXiv versions are updated less often.

B1. [PDF] The arithmetic of quaternion algebras, book in preparation (still very rough!).
 
31. [PDF] [1209.2460] Lattice methods for algebraic modular forms on classical groups (with Matthew Greenberg), accepted to "Computations with modular forms".
30. Minimal isospectral and nonisometric 2-orbifolds (with Peter Doyle and Benjamin Linowitz), in preparation.
29. [PDF] [1205.0045] Computing power series expansions of modular forms (with John Willis), accepted to "Computations with modular forms".
28. On computing Belyi maps, in preparation.
27. The monoid of quadratic rings, in preparation.
26. [PDF] [1010.5727] [Errata] Explicit methods for Hilbert modular forms (with Lassina Dembélé), accepted to "Elliptic curves, Hilbert modular forms and Galois deformations".
25. [PDF] [1003.3512] Rings of low rank with a standard involution, accepted to Illinois J. Math.
24. The canonical ring of a stacky curve (with David Zureick-Brown), in preparation.
23. Tables of Hilbert modular forms and elliptic curves over totally real fields (with Steve Donnelly), in preparation.
22. [PDF] [1004.5340] [Errata] [Link] Computing automorphic forms on Shimura curves over fields with arbitrary class number, Algorithmic number theory (ANTS IX, Nancy, France, 2010), eds. Guillaume Hanrot, Francois Morain, and Emmanuel Thomé, Lecture Notes in Comp. Sci., vol. 6197, Springer, Berlin, 2010, 357-371.
21. [PDF] [0907.2060] Nondegenerate curves of low genus over small finite fields (with Wouter Castryck), Arithmetic, Geometry, Cryptography and Coding Theory 2009, Contemporary Mathematics, vol. 521, Amer. Math. Soc., Providence, RI, 2010, 21-28.
20. [PDF] [0906.4374] [Link] Nonsolvable number fields ramified only at 3 and 5 (with Lassina Dembélé and Matthew Greenberg), Compositio Math. 149 (2011), no. 3, 716-734.
19. [PDF] [0904.4310] [Errata] [Link] Characterizing quaternion rings over an arbitrary base, J. Reine Angew. Math. 657 (2011), 113-134.
18. [PDF] [0904.3908] [Link] Computing systems of Hecke eigenvalues associated to Hilbert modular forms (with Matthew Greenberg), Math. Comp. 80 (2011), 1071-1092.
17. [PDF] Algebraic curves uniformized by congruence subgroups of triangle groups (with Pete L. Clark), preprint.
16. [PDF] [1112.4881] [Link] [Errata] Computing zeta functions of nondegenerate hypersurfaces with few monomials (with Steven Sperber), LMS J. Comp. Math. 16 (2013), 9-44.
15. [PDF] [1004.0994] Identifying the matrix ring: algorithms for quaternion algebras and quadratic forms, accepted to "Quadratic and higher degree forms".
14. [PDF] [0808.3833]
[Link]
[Tables]
[Corrigendum]		 Algorithmic enumeration of ideal classes for quaternion orders (with Markus Kirschmer), SIAM J. Comput. (SICOMP) 39 (2010), no. 5, 1714-1747.
13. [PDF] [0806.0306] [Link] The Gauss higher relative class number problem, Ann. Sci. Math. Québec 32 (2008), no. 2, 221-232.
12. [PDF] [0802.0911]
[Link] [Tables]
[Errata]		 Shimura curves of genus at most two, Math. Comp. 78 (2009), 1155-1172.
11. [PDF] [0802.0196] [Link]
[Demo]
[Errata]		 Computing fundamental domains for Fuchsian groups, J. Théorie Nombres Bordeaux 21 (2009), no. 2, 467-489.
10. [PDF] [0802.0420]
[Link]
[Errata]		 On nondegeneracy of curves (with Wouter Castryck), Algebra & Number Theory 3 (2009), no. 3, 255-281.
9. [PDF] [0802.0194]
[Link]
[Tables]
Enumeration of totally real number fields of bounded root discriminant, Algorithmic number theory (ANTS VIII, Banff, 2008), eds. Alfred van der Poorten and Andreas Stein, Lecture Notes in Comp. Sci., vol. 5011, Springer, Berlin, 2008, 268-281.
8. [PDF] Shimura curve computations, Arithmetic Geometry, Clay Math. Proc., vol. 8, Amer. Math. Soc., Providence, 2009, 103-113.
7. [PDF] Heegner points and Sylvester's conjecture (with Samit Dasgupta), Arithmetic Geometry, Clay Math. Proc., vol. 8, Amer. Math. Soc., Providence, 2009, 91-102.
6. [PDF] [0410266]
[Errata] [Link] 		Quadratic forms that represent almost the same primes, Math. Comp. 76 (2007), 1589-1617.
5. [PDF] [Link]
[Errata]		 Computing CM points on Shimura curves arising from cocompact arithmetic triangle groups, Algorithmic number theory (ANTS VII, Berlin, 2006), eds. Florian Hess, Sebastian Pauli, Michael Pohst, Lecture Notes in Comp. Sci., vol. 4076, Springer, Berlin, 2006, 406-420.
4. Arithmetic Fuchsian groups and Shimura curves, Quaternion algebras (with David Kohel), Associative orders (with Nicole Sutherland), Handbook of Magma functions, eds. John Cannon and Wieb Bosma, Sydney, ed. 2.14, 2007.
3. [PDF] Curves over finite fields with many points: an introduction, Computational aspects of algebraic curves, ed. Tanush Shaska, Lecture Notes Series on Computing, vol. 13, World Scientific, Hackensack, NJ, 2005, 124-144.
2. [PDF] Quadratic forms and quaternion algebras: Algorithms and arithmetic, Ph.D. thesis, University of California, Berkeley, 2005.
1. [PDF] On the nonexistence of odd perfect numbers, MASS Selecta: Teaching and learning advanced undergraduate mathematics, Svetlana Katok, Alexei Sossinsky, and Serge Tabachnikov, eds., American Mathematical Society, Providence, RI, 2003, 293-300.

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