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 stateoftheart image compression, IEEE International Conference on Image Processing (ICIP), 2014, pp. 4092–4096.
13. (with L.H. Lim) Most tensor problems
are NPhard, 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 skewsymmetric 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): 6179. pdf  arXiv
10. (with S. Sullivant) Finite Groebner
bases in infinite dimensional polynomial rings
and applications, Advances in Mathematics, 221 (2012) 125. pdf  arXiv
9. (with GarciaPuente, Martin del
Campo, Ruffo, Teitler, Johnson, and Sottile) Experimentation
at the Frontiers of Reality in Schubert Calculus, Contemporary Mathematics, 517 (2010), 365380. 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), 7376. arxiv
 pdf
7. (with T. Windfeldt). An algebraic
characterization of uniquely vertex colorable
graphs, Journal of Combinatorial Theory Series
B, 98 (2008), 400414. 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, 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
4. (with L. Levine) Polynomial
recurrences and cyclic resultants, Proceedings
of the American Mathematical Society, 135 (2007), 16071618. arXiv
 pdf
 AMS
3. (with M. Aschenbrenner) Finite
generation of symmetric ideals, Transactions
of the American Mathematical Society, 359 (2007), 51715192. arXiv
 pdf
 (minor errata
here)
2. Cyclic Resultants, Journal
of Symbolic Computation, 39
(2005), 653669; 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, 945953. arXiv
 pdf
 ps
