Curriculum Vitae

Lenny Fukshansky


Address

         Department of Mathematics
         Claremont McKenna College
         850 Columbia Avenue
         Claremont, CA 91711

         Phone: (909) 607 - 0014
         Fax:     (909) 621 - 8419
         Email: lenny@cmc.edu
         Webpage:  http://math.cmc.edu/lenny/

Personal
Education
University of Texas at Austin
Advisor: Prof. J. D. Vaaler
Thesis:   Algebraic points of small height with additional arithmetic conditions
University of California at Los Angeles
Professional Experience
Visiting Positions
Invited Research Visits
Research Interests
   

    Number theory, arithmetic geometry, discrete and convex geometry, in particular:
Publications
  1. Small zeros of quadratic forms with linear conditions, Journal of Number Theory, vol. 108 no. 1 (2004), pg. 29-43
  2. Lattice points in homogeneously expanding compact domains, One section of the omnibus Problems Article "Problems from the Cottonwood Room" (M. Beck, B. Chen, L. Fukshansky, C. Haase, A. Knutson, B. Reznick, S. Robins, A. Schuermann),  Contemporary Mathematics 374 (2005), 179-191, Proceedings of the Summer 2003 AMS/MAA/SIAM Conference on Integer Points in Polyhedra
  3. Integral points of small height outside of a hypersurface, Monatshefte für Mathematik, vol. 147 no. 1 (2006), pg. 25-41
  4. Siegel's lemma with additional conditions, Journal of Number Theory, vol. 120 no. 1 (2006), pg. 13-25
  5. (with Sinai Robins) Frobenius problem and the covering radius of a lattice, Discrete and Computational Geometry, vol. 37 no. 3 (2007), pg. 471-483
  6. On effective Witt decomposition and Cartan-Dieudonné theorem, Canadian Journal of Mathematics, vol. 59 no. 6 (2007), pg. 1284-1300
  7. Small zeros of quadratic forms over the algebraic closure of Q, International Journal of Number Theory, vol. 4 no. 3 (2008), pg. 503-523
  8. On distribution of well-rounded sublattices of Z^2, Journal of Number Theory, vol. 128 no. 8 (2008), pg. 2359-2393
  9. On similarity classes of well-rounded sublattices of Z^2, Journal of Number Theory, vol. 129 no. 10 (2009), pg. 2530-2556
  10. Search bounds for zeros of polynomials over the algebraic closure of Q, Rocky Mountain Journal of Mathematics, vol. 39, no. 3 (2009), pg. 789-804
  11. Effective structure theorems for symplectic spaces via height, in "Quadratic forms -- algebra, arithmetic, and geometry" (R. Baeza, W.K. Chan, D.W. Hoffmann, and R. Schulze-Pillot, eds.), Contemporary Mathematics 493 (2009), pg. 117--130
  12. Integral orthogonal bases of small height for real polynomial spaces, Online Journal of Analytic Combinatorics, vol. 4 (2009), art. 7, 10 pp.
  13. (with Wai Kiu Chan) Small zeros of hermitian forms over quaternion algebras, Acta Arithmetica, vol. 142 no. 3 (2010), pg. 251--266
  14. Algebraic points of small height missing a union of varieties, Journal of Number Theory, vol. 130 no. 10 (2010), pg. 2099--2118 -- an earlier version of this paper also appears in the MPIM Preprint Series
  15. (with D. Moore, A. Ohana, W. Zeldow) On well-rounded sublattices of the hexagonal latticeDiscrete Mathematics, vol. 310 no. 23 (2010), pg. 3287--3302
  16. Revisiting the hexagonal lattice: on optimal lattice circle packing, Elemente der Mathematik, vol. 66 no. 1 (2011) pg. 1--9
  17. (with Sinai Robins) Bounds for solid angles of lattices of rank three, Journal of Combinatorial Theory A, vol. 118 no. 2 (2011), pg. 690--701
  18. (with Achill Schuermann) Bounds on generalized Frobenius numbers, European Journal of Combinatorics, vol. 32 no. 3 (2011) pg. 361--368
  19. (with Kate Petersen) On well-rounded ideal lattices, International Journal of Number Theory, vol. 8 no. 1 (2012) pg. 189--206
  20. (with G. Henshaw, P. Liao, M. Prince, X. Sun, S. Whitehead) On integral well-rounded lattices in the plane, Discrete and Computational Geometry, vol. 48 no. 3 (2012), pg. 735--748
  21. (with Iskander Aliev and Martin Henk) Generalized Frobenius numbers: bounds and average behavior, Acta Arithmetica, vol. 155 no. 1 (2012), pg. 53--62
  22. (with G. Henshaw, P. Liao, M. Prince, X. Sun, S. Whitehead) On well-rounded ideal lattices - II, International Journal of Number Theory, vol. 9 no. 1 (2013) pg. 139--154
  23. Heights and quadratic forms: on Cassels' theorem and its generalizations, in "Diophantine methods, lattices, and arithmetic theory of quadratic forms" (W. K. Chan, L. Fukshansky, R. Schulze-Pillot, and J. D. Vaaler, eds.), Contemporary Mathematics, AMS vol. 587 (2013), pg. 77--94
  24. (with Glenn Henshaw) Lattice point counting and height bounds over number fields and quaternion algebras, Online Journal of Analytic Combinatorics, vol. 8 (2013), art. 4, 20 pp.
  25. Well-rounded zeta-function of planar arithmetic lattices, Proceedings of the American Mathematical Society, vol. 142 no. 2 (2014), pg. 369--380
  26. (with Wai Kiu Chan and Glenn Henshaw) Small zeros of quadratic forms missing a union of varieties, to appear in the Transactions of the AMS
  27. (with Hiren Maharaj) Lattices from elliptic curves over finite fields, Finite Fields and Their Applications, vol. 28 (July 2014), pg. 67--78
  28. (with Xun Sun) On the geometry of cyclic lattices,  submitted for publication
  29. Stability of ideal lattices from quadratic number fields,  to appear in the Ramanujan Journal
  30. (with Wai Kiu Chan and Glenn Henshaw) Totally isotropic subspaces of small height in quadratic spaces, submitted for publication

Editorial

Honors, Awards, Scholarships, Funding
Invited talks
Contributed talks
Educational and expository talks
Seminar talks
Other special programs and conferences attended
Research supervision

Postdoctoral fellows supervision
Ph.D. students
Ph.D. thesis committee service
Undergraduate thesis and research supervision

Research programs supervision

Professional activities and service

Organizing activities

Reviewing and refereeing service

Special Teaching and Outreach Activities
Courses Taught
Lecture Notes (available on the webpage in PDF format)
Computing Skills