Current Research Interests:
Structured polynomial
systems, computational algebraic geometry,
combinatorics,
matrix analysis, applications of mathematics to
neuroscience
Short cv.
Some Selected Publications:
(with D. Rhea). Automorphisms of finite abelian
groups, American Mathematical Monthly,
114 (2007), no. 10, 917923. pdf  arXiv
 Wikipedia
1. Sums of polynomial squares
over totally real fields are rational sums of
squares, Proceedings of the American Mathematical
Society, 137 (2009),
921930. pdf
2. (with J. Nie) An elementary
and constructive solution to Hilbert's 17th Problem
for matrices, Proceedings of the American
Mathematical Society, 136
(2008), 7376. arxiv
 pdf
3. (with T. Windfeldt). An algebraic
characterization of uniquely vertex colorable
graphs, Journal of Combinatorial Theory Series
B, 98 (2008), 400414. pdf
 arXiv
 code
4. (with S. Armstrong). Solvability
of symmetric word equations in positive definite
letters, Journal of the London Mathematical
Society, 76 (2007),
no. 3, 777796. arXiv
 pdf
 maple
code 1  maple
code 2
5. Advances on the The BessisMoussaVillani
Trace Conjecture, Linear Algebra and Applications,
426 (2007), 130142. arXiv
 pdf
 LinAlgAppl
6. (with L. Levine) Polynomial
recurrences and cyclic resultants, Proceedings
of the American Mathematical Society, 135 (2007), 16071618. arXiv
 pdf
 AMS
7. (with M. Aschenbrenner) Finite
generation of symmetric ideals, Transactions
of the American Mathematical Society, 359 (2007), 51715192. arXiv
 pdf
 (minor errata
here)
8. Cyclic Resultants, Journal
of Symbolic Computation, 39
(2005), 653669; erratum, ibid. 40 (2005), 1126–1127. arXiv
 pdf
 errata
to print version
9. Logarithmic Derivatives of
Solutions to Linear Differential Equations, Proceedings
of the American Mathematical Society, 132 (2004), no. 9, 26932701. arXiv
 pdf
 ps
 AMS
(an expanded and more expository version is here).
10. (with C. R. Johnson).
Symmetric word equations in two positive definite
letters, Proceedings of the American Mathematical
Society 132 (2004), no.
4, 945953. arXiv
 pdf
 ps
