
John Voight
Assistant Professor
Department of Mathematics and Statistics
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/~voight/
Office hours: Mondays, 11:00 a.m. - 12:00 noon and 1:00 p.m. - 2:00 p.m.; Wednesdays, 11:00 a.m. - 12:00 noon; or by appointment!
Research Interests:
- Arithmetic algebraic geometry: Modular curves and moduli spaces, Shimura curves, elliptic curves, computational and algorithmic aspects
- Number theory: Algebraic number theory, quaternion algebras, Arakelov theory, zeta functions of varieties over finite fields, cryptography and coding theory
Teaching:
Past Courses:
Vitae:
Publications:
- Algorithms for quaternion algebras, in preparation.
- Shimura curves of genus at most two, accepted to Math. Comp.
[math.NT/0802.0911]
[DVI]
[PS]
[PDF]
See also the resulting tables.
- Computing fundamental domains for cofinite Fuchsian groups, submitted.
[math.NT/0802.0196]
[PS]
[PDF]
- On moduli of nondegenerate curves (with Wouter Castryck), submitted.
[math.AG/0802.0420]
[DVI]
[PS]
[PDF]
- Enumeration of totally real number fields of bounded root discriminant, accepted to Lecture Notes in Comp. Sci. (ANTS VIII).
[math.NT/0802.0194]
[DVI]
[PS]
[PDF]
See also the resulting tables.
- Shimura curve computations, to appear in proceedings from the 2006 Clay Mathematics Institute, Arithmetic Geometry summer school.
[DVI]
[PS]
[PDF]
- Heegner points and Sylvester's conjecture (with Samit Dasgupta),
to appear in proceedings from the 2006 Clay Mathematics Institute, Arithmetic Geometry summer school.
[DVI]
[PDF]
- Quadratic forms that represent almost the same primes, Math. Comp. 76 (2007), 1589-1617.
[math.NT/0410266]
[Linked PDF]
[DVI]
[PS]
[PDF]
- Computing CM points on Shimura curves arising from cocompact arithmetic triangle groups, Algorithmic number theory, eds. Florian Hess, Sebastian Pauli, Michael Pohst,
Lecture notes in computer science, vol. 4076, Springer, Berlin, 2006, 406-420.
[Link]
[PS]
[PDF]
- 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.
- 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.
[DVI]
[PDF]
[PS]
- Quadratic forms and quaternion algebras: Algorithms and arithmetic, Ph.D. thesis, University of California, Berkeley, 2005.
[DVI]
[PDF]
[PS]
- 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.
[PDF]
Tables:

Notes and Expository Articles:
- Perfect numbers: An elementary introduction
[DVI]
[PDF]
[PS]
- Introduction to stacks
[DVI]
[PDF]
[PS]
- Toric surfaces and continued fractions
[DVI]
[PDF]
[PS]
- Oberwolfach seminar on Explicit Algebraic Number Theory
[Link to Notes]
- Aspects of complex multiplication (notes from Zagier)
[DVI]
[PDF]
[PS]
- Introduction to group schemes (notes from Schoof)
[DVI]
[PDF]
[PS]
- Rational and integral points on higher dimensional varieties (notes from AIM)
[Link to Notes]
- Algebraic geometry (notes from Hartshorne)
[DVI]
[PDF]
[PS]
The following counter is due to digits.com.