Lenny Fukshansky

• Citizenship: USA
• Born in Leningrad, Russia
  
• Fluent in Russian (native) and English languages
• Member of AMS
  

• Ph.D. in Mathematics, August 2004

University of Texas at Austin
Advisor: Prof. J. D. Vaaler

• B.S. in Applied Mathematics with Specialization in Computing, 1995

University of California at Los Angeles

• Assistant Professor, Claremont McKenna College, 2007 - present
  
• Visiting Assistant Professor, Texas A&M University, 2004 - 2007
  
• Assistant Instructor and Teaching Assistant, University of Texas at Austin, 1998 - 2004
  
• Teaching Assistant, University of Nebraska at Lincoln, Spring 1998
  
• Software Engineer, IBM, General Magic, Compuware, and Compaq corporations, 1995 - 1998

• Institut des Hautes Etudes Scientifique (IHES), Bures-sur-Yvette, France, July 2007
  
• Max Planck Institut für Mathematik (MPI), Bonn, Germany, July/August 2006

• Diophantine approximations, equations, and problems
• Classical and adelic geometry of numbers
• Quadratic and linear forms; polynomials
  
• Theory of height functions, rational points on varieties, Mahler's measure, and connections with arithmetic geometry
• Geometric combinatorics, lattice point counting, Erhart polynomial
• Lattices, linear Diophantine problem of Frobenius
  

1. Algebraic points of small height with additional arithmetic conditions, Ph.D. Thesis, University of Texas at Austin, August 2004
2. Small zeros of quadratic forms with linear conditions, Journal of Number Theory, vol. 108 no. 1 (2004), pg. 29-43
3. 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
   
4. Integral points of small height outside of a hypersurface, Monatshefte für Mathematik, vol. 147 no. 1 (2006), pg. 25-41
5. Siegel's lemma with additional conditions, Journal of Number Theory, vol. 120 no. 1 (2006), pg. 13-25
6. (with Sinai Robins) Frobenius problem and the covering radius of a lattice, Discrete and Computational Geometry, vol. 37 no. 3 (2007), pg. 471-483
7. On effective Witt decomposition and Cartan-Dieudonné theorem, to appear in Canadian Journal of Mathematics
8. Search bounds for zeros of polynomials over the algebraic closure of Q, to appear in Rocky Mountain Journal of Mathematics
   
9. Small zeros of quadratic forms over the algebraic closure of Q, to appear in International Journal of Number Theory
10. On distribution of well-rounded sublattices of Z^2, submitted for publication
11. On similarity classes of well-rounded sublattices of Z^2, submitted for publication

• AMS/NSF travel grant for ICM 2006, August 2006
  
• NSF VIGRE postdoctoral fellowship, Texas A&M University, 2004-2005
  
• Graduate Research Assistanship,  University of Texas at Austin, Summer 2002
• NSF VIGRE traveling support, University of Texas at Austin, December 2001
  
• Dodd Teaching Excellence Award,  Department of Mathematics, University of Texas at Austin, 2000
• First year summer fellowship, Department of Mathematics, University of Texas at Austin, 1999
• CalGrant Scholarship, University Scholarship, and College of Letters and Science Honors, UCLA, 1992-1993

• Frobenius number, covering radius, and well-rounded lattices, Colloquium, George Mason University, February 2007
  
• Frobenius number, covering radius, and well-rounded lattices, Colloquium, Bucknell University, February 2007
• Frobenius number, covering radius, and well-rounded lattices, Colloquium, Claremont McKenna College, January 2007
  
• Effective decompositions of quadratic spaces via heights, Number Theory Seminar, Max Planck Institut für Mathematik - Bonn, July 2006
  
• Frobenius number, covering radius, and ESM lattices, Number Theory Seminar, University of Göttingen, June 2006
  
• Quadratic forms and height functions, Colloquium of the Graduiertenkolleg, University of Göttingen, June 2006
  
• On the linear Diophantine problem of Frobenius, Oberseminar des Institutes für Algebra und Geometrie , University of Magdeburg, June 2006
  
• On the Frobenius problem, Algebra-Geometry-Combinatorics Seminar, San Francisco State University, May 2006
  
• Frobenius number of ESM lattices, Number Theory Seminar, University of Texas at Austin, February 2006
  
• The Frobenius problem and the covering radius of a lattice, Colloquium, Temple University, February 2006
  
• Effective theorems for quadratic spaces over the algebraic closure of Q, AMS Special Session on Mahler Measure and Heights, Joint Mathematics Meeting, San Antonio, TX, January 2006
  
• Effective structure theorems for quadratic spaces and their isometries, Number Theory Seminar, University of Illinois at Urbana-Champaign, February 2005
  
• Heights and Diophantine problems, Colloquium, Rice University, September 2004
• Small zeros of quadratic polynomials, Number Theory Seminar, Texas A&M University, November 2003
• Small zeros of quadratic forms with linear conditions, Mahler's Measure of Polynomials Conference, Simon Fraser University, June 2003

• Effective theorems for quadratic spaces via height, Seminaire de theorie des nombres de Chevaleret, Institut de Mathématiques de Jussieu, Paris, France, July 2007
  
• On distribution of integral well-rounded lattices in dimension two, Illinois Number Theory Fest, May 2007
  
• Effective theorems for quadratic spaces, ICM 2006, Madrid, Spain, August 2006
  
• Frobenius problem and the covering radius of a lattice, West Coast Number Theory, Pacific Grove, CA, December 2005
  
• Some effective Diophantine results over the algebraic closure of Q, XXIVth Journées Arithmétiques, Marseilles, France, July 2005
  
• Effective decompositions of quadratic spaces, ArithmeTexas, College Station, TX, April 2005
  
• Counting lattice points in admissible adelic sets, MNTCG2, Urbana-Champaign, IL, February 2005
  
• On effective Witt decomposition and Cartan-Dieudonné theorem, West Coast Number Theory Conference, Las Vegas, NV, December 2004
  
• Siegel's lemma with additional conditions, CNTA8, Toronto, June 2004
• Integral points of small height outside of a hypersurface, Illinois Number Theory Conference, Urbana-Champaign, May 2004
• Lattice points of small height in projective varieties, Integer points in polyhedra, Joint Summer research conferences, Snowbird, Utah, July 2003
• On a Discrete Analogue of the Tarski Plank Problem, West Coast Number Theory Conference, SFSU, San Francisco, December 2002
• Points of small height outside of a collection of subspaces, CNTA7, Montreal, Canada, May 2002
• Small Zeros of Quadratic Forms over a Number Field, West Coast Number Theory Conference, Pacific Grove, CA, December 2001

• Mahler's measure and Lehmer's conjecture, Mathematics Graduate Student Organization Seminar, Texas A&M University, October 2006
  
• Packing oranges and constructing error correcting codes, invited lecture to school students as a part of Math Awareness Month, Texas A&M University, April 2006
  
• Simultaneous Diophantine approximations and a conjecture of Minkowski, Introduction to Mathematical Research seminar series, University of Texas at Austin, March 2006
  
• Semester review of calculus, invited lecture to freshmen engineering students as a part of Texas A&M Leaders in Freshman Engineering final review series, December 2005
  
• Diophantine equations: the mystery of numbers, invited lecture to high school students as a part of Texas A&M Summer Honors Invitational Program (SHIP), June 2005
  

• On the distribution of integral well-rounded lattices in dimension two, Part II, Number Theory Seminar, Texas A&M University, February 2007
  
• On the distribution of integral well-rounded lattices in dimension two, Number Theory Seminar, Texas A&M University, September 2006
  
• Effective theorems for quadratic spaces over Q-bar, Number Theory Seminar, Texas A&M University, January 2006
  
• The Frobenius problem and the covering radius of a lattice, Number Theory Seminar, Texas A&M University, October 2005
  
• Some effective Diophantine results over Q-bar, Number Theory Seminar, Texas A&M University, April 2005
  
• On effective Witt decomposition and Cartan-Dieudonné theorem, Number Theory Seminar, Texas A&M University, September 2004
  
• Points of small height with arithmetic conditions, Number Theory Seminar, University of Texas at Austin, November 2003

• SMS-NATO ASI 2005: Equidistribution in Number Theory, Montreal, Canada, July 2005
  
• Arizona Winter School: Number Theory and Physics, Austin, TX, March 2004
• NSF-CBMS Special Program: Web of Modularity, Urbana, IL, June 2003
• MSRI Summer Program: Excursions in Computational Number Theory - Polynomials with integer coefficients, Vancouver, Canada, June 2002; Project and presentation: Heights of products of cyclotomic polynomials
• Illinois Number Theory Conference, Urbana, IL, May 2002
• Arizona Winter School: Periods, Tucson, AZ, March 2002

• Referee for Journal of Number Theory, Canadian Mathematical Bulletin
  
• Reviewer for Mathematical Reviews
• Organizer for the Number Theory seminar, Texas A&M University, 2006-2007
• Organizer for the Working Number Theory seminar, Texas A&M University, 2004 - 2005
• Graduate committee member for MS thesis committees of Mr. Ayodeji Alajo and Mr. Dae Hwan Lee, Texas A&M University
  

• Speaker and contest problem grader for Math Awareness event for elementary, middle, and high school students, 2006
  
• Assistant Instructor for an REU/VIGRE course, 2005
  
• Participated in Texas A&M Summer Honors Invitational Program (SHIP) for high school students, 2005
  
• Instructor for Emerging Scholars Program (ESP), 2001-2002
• Instructor for Supplemental Instruction Program (SI), 2001

• Diophantine Approximations and Geometry of Numbers (graduate special topics course), Texas A&M University, Instructor
• Linear Algebra (Honors) for math and science majors, Texas A&M University, Instructor
• Linear Algebra for engineering majors, Texas A&M University, Instructor
• Analytic Geometry and Calculus for math and science majors, Texas A&M University, Instructor
• Engineering Calculus II (Honors), Texas A&M University, Instructor
• REU/VIGRE Course: Algebraic Methods in Computational Biology, Texas A&M University, Assistant Instructor
• Methods of Applied Mathematics I (graduate course), Texas A&M University, Instructor
  
• Elementary Functions and Coordinate Geometry (Precalculus), University of Texas at Austin, Instructor
  
• Differential and Integral Calculus (first and second semesters), University of Texas at Austin, Teaching Assistant
  
• Calculus for Business and Economics, University of Texas at Austin, Teaching Assistant
• Differential Equations, University of Texas at Austin, Teaching Assistant

• Various UNIX-type operating systems, Windows, Mac OS
• C, C++, Java, SQL, and other programming languages
• TCP/IP, SGI, ASP, and other communication protocols
• DB2, Oracle, and other database systems