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Reseach


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, 917-923. 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), 921-930. 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), 73-76. arxiv | pdf

3. (with T. Windfeldt). An algebraic characterization of uniquely vertex colorable graphs, Journal of Combinatorial Theory Series B, 98 (2008), 400-414. 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, 777-796. arXiv | pdf | maple code 1 | maple code 2

5. Advances on the The Bessis-Moussa-Villani Trace Conjecture, Linear Algebra and Applications, 426 (2007), 130-142. arXiv | pdf | LinAlgAppl

6. (with L. Levine)  Polynomial recurrences and cyclic resultants, Proceedings of the American Mathematical Society, 135 (2007), 1607-1618.  arXiv | pdf | AMS

7. (with M. Aschenbrenner) Finite generation of symmetric ideals, Transactions of the American Mathematical Society, 359 (2007), 5171-5192.  arXiv | pdf | (minor errata here)

8. Cyclic Resultants, Journal of Symbolic Computation, 39 (2005), 653-669; 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, 2693-2701. 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, 945-953. arXiv | pdf | ps







































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