Current Research Interests:
Structured polynomial
systems, computational algebraic geometry,
combinatorics,
matrix analysis, applications of mathematics to
neuroscience
Short cv.
Some Selected Research Publications:
14. (with Ram Mehta and Kilian Koepsell) A Hopfield recurrent neural network trained on natural images performs state-of-the-art image compression, IEEE International Conference on Image Processing (ICIP), 2014, pp. 4092–4096.
13. (with L.H. Lim) Most tensor problems
are NP-hard, Journal of the ACM, 60 (2013), no. 6, Art. 45, 39 pp. pdf | Ex 1.5 SINGULAR code | Appendix SINGULAR code, Macaulay 2 code
12. (with F. Sottile)
Static skew-symmetric output feedback control, SIAM Journal on Control and Optimization, 51 (2013), Issue 4. pdf | arXiv
11. (with L. Levine and D. Rhea) Equations solvable by radicals in a uniquely divisible group, Bulletin of the London Mathematical Society, (2012) 45 (1): 61-79. pdf | arXiv
10. (with S. Sullivant) Finite Groebner
bases in infinite dimensional polynomial rings
and applications, Advances in Mathematics, 221 (2012) 1-25. pdf | arXiv
9. (with Garcia-Puente, Martin del
Campo, Ruffo, Teitler, Johnson, and Sottile) Experimentation
at the Frontiers of Reality in Schubert Calculus, Contemporary Mathematics, 517 (2010), 365-380. pdf | arXiv
8. (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
7. (with T. Windfeldt). An algebraic
characterization of uniquely vertex colorable
graphs, Journal of Combinatorial Theory Series
B, 98 (2008), 400-414. pdf
| arXiv
| code
6. (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
4. (with L. Levine) Polynomial
recurrences and cyclic resultants, Proceedings
of the American Mathematical Society, 135 (2007), 1607-1618. arXiv
| pdf
| AMS
3. (with M. Aschenbrenner) Finite
generation of symmetric ideals, Transactions
of the American Mathematical Society, 359 (2007), 5171-5192. arXiv
| pdf
| (minor errata
here)
2. Cyclic Resultants, Journal
of Symbolic Computation, 39
(2005), 653-669; erratum, ibid. 40 (2005), 1126–1127. arXiv
| pdf
| errata
to print version
1. (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
|
