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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

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

Education

Ph.D. in Mathematics, August 2004

University of Texas at Austin
Advisor: Prof. J. D. Vaaler
Thesis: Algebraic points of small height with additional arithmetic conditions

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

University of California at Los Angeles

Professional Experience

Member of Extended Graduate Faculty, Claremont Graduate University, January 2010 - present
Associate Professor (with tenure), Claremont McKenna College, December 2009 - present
Assistant Professor, Claremont McKenna College, July 2007 - December 2009
Visiting Assistant Professor, Texas A&M University, September 2004 - August 2007
Assistant Instructor and Teaching Assistant, University of Texas at Austin, September 1998 - August 2004
Teaching Assistant, University of Nebraska at Lincoln, Spring 1998
Software Engineer, IBM, General Magic, Compuware, and Compaq corporations, 1995 - 1998

Visiting Positions

Institut des Hautes Etudes Scientifique (IHES), Bures-sur-Yvette, France, October/November 2010
Max Planck Institut für Mathematik (MPIM), Bonn, Germany, June 2008
Institut des Hautes Etudes Scientifique (IHES), Bures-sur-Yvette, France, July 2007
Max Planck Institut für Mathematik (MPIM), Bonn, Germany, July/August 2006

Invited Research Visits

Nanyang Technological University, Singapore, 2 weeks in May 2009
Wesleyan University, Middletown, CT, USA, 2 weeks in July/August 2008

Research Interests

Number theory, arithmetic geometry, discrete and convex geometry, in particular:

Diophantine approximation, 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, packings and coverings, linear Diophantine problem of Frobenius

Publications

Small zeros of quadratic forms with linear conditions, Journal of Number Theory, vol. 108 no. 1 (2004), pg. 29-43
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
Integral points of small height outside of a hypersurface, Monatshefte für Mathematik, vol. 147 no. 1 (2006), pg. 25-41
Siegel's lemma with additional conditions, Journal of Number Theory, vol. 120 no. 1 (2006), pg. 13-25
(with Sinai Robins) Frobenius problem and the covering radius of a lattice, Discrete and Computational Geometry, vol. 37 no. 3 (2007), pg. 471-483
On effective Witt decomposition and Cartan-Dieudonné theorem, Canadian Journal of Mathematics, vol. 59 no. 6 (2007), pg. 1284-1300
Small zeros of quadratic forms over the algebraic closure of Q, International Journal of Number Theory, vol. 4 no. 3 (2008), pg. 503-523

On distribution of well-rounded sublattices of Z^2, Journal of Number Theory, vol. 128 no. 8 (2008), pg. 2359-2393
On similarity classes of well-rounded sublattices of Z^2, Journal of Number Theory, vol. 129 no. 10 (2009), pg. 2530-2556
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
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
Integral orthogonal bases of small height for real polynomial spaces, Online Journal of Analytic Combinatorics, no. 4 (2009), art. 7, 10 pp.
(with Wai Kiu Chan) Small zeros of hermitian forms over quaternion algebras, Acta Arithmetica, vol. 142 no. 3 (2010), pg. 251--266
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
Revisiting the hexagonal lattice: on optimal lattice circle packing, to appear in Elemente der Mathematik
(with Sinai Robins) Bounds for solid angles of lattices of rank three, to appear in the Journal of Combinatorial Theory A
(with D. Moore, A. Ohana, W. Zeldow) On well-rounded sublattices of the hexagonal lattice, to appear in Discrete Mathematics
(with Achill Schurmann) Bounds on generalized Frobenius numbers, submitted for publication

Honors, Awards, Scholarships, Funding

Faculty Research Grant, Claremont McKenna College, Fall 2010
Senior personnel on NSF grant DMS-0755540: REU program for Claremont Colleges, 2008-2011
Faculty Research Grant, Claremont McKenna College, Summer 2008
Teaching Resource Center mini-grant, Claremont McKenna College, Spring 2008
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

Invited talks

On the Frobenius problem and covering radius of a lattice, Combinatorics Seminar, UCLA, May 2010
On distribution of well-rounded lattices in the plane, Number Theory Seminar, UC Irvine, March 2010
Small zeros of hermitian forms over quaternion algebras, AMS-KMS Special Session: Arithmetic of quadratic forms, First Joint Meeting of AMS and Korean Mathematical Society, Seoul, South Korea (December 16-20, 2009) -- CANCELLED
On the Frobenius coin-exchange problem, Graduate Seminar, California State University Channel Islands, Camarillo, CA, September 2009
Points of small height missing a union of varieties, AMS Special Session: Algebra and Number Theory with Polyhedra, AMS Spring Western Section Meeting, San Francisco, CA, February 2009
Siegel's lemma outside of a union of varieties, AMS Special Session: Number Theory, AMS Fall Eastern Section Meeting, Middletown, CT, October 2008
On distribution of well-rounded sublattices of Z^2, Séminaire de Théorie des Nombres, Institut de Mathématiques de Bordeaux, University of Bordeaux, France, June 2008
On similarity classes of well-rounded sublattices of Z^2, Oberseminar des Institutes für Algebra und Geometrie, University of Magdeburg, Germany, June 2008
On zeta function of well-rounded sublattices of Z^2, Number Theory Seminar, Institut de Mathématiques de Jussieu, Paris, France, May 2008
Sphere packing, lattices, and Epstein zeta function, Colloquium, California State University at Los Angeles, April 2008
Sphere packing, lattices, and Epstein zeta function, Colloquium, California State University at Northridge, March 2008
Frobenius number, covering radius, and well-rounded lattices, AMS Special Session: The linear Diophantine problem of Frobenius, Joint Mathematics Meeting, San Diego, CA, January 2008
Effective structure theorems for quadratic spaces via height, Second International Conference on The Algebraic and Arithmetic Theory of Quadratic Forms 2007, Lake Llanquihue, Chile, December 2007
Sphere packing, lattices, and Epstein zeta function, Claremont Mathematics Colloquium, Claremont Colleges, November 2007
Effective theorems for quadratic spaces via height, Number Theory Seminar, UCLA, October 2007
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

Contributed talks

Orthogonal Siegel's lemma, Illinois Number Theory Conference, May 2010
Algebraic points of small height missing a union of varieties, Western Number Theory Conference, Fort Collins, CO, December 2008
Siegel's lemma outside of a union of varieties, Number Theory Seminar, UCLA, November 2008
On distribution of well-rounded sublattices of Z^2, CNTA10, Waterloo, Canada, July 2008
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

Educational and expository talks

Math in the grocery aisle: from stacking oranges to constructing error-correcting codes, invited lecture at GEMS: Gateway to Exploring Mathematical Sceinces, Claremont Colleges, February 2009
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

Seminar talks

Revisiting the hexagonal lattice: on optimal lattice circle packing, Algebra / Number Theory / Combinatorics Seminar, Claremont Colleges, February 2010
On minimal lattice spherical configurations in three dimensions, Topology and Geometry seminar, Claremont Colleges, November 2009
Diophantine approximation on a circle, Analysis Seminar, Claremont Colleges, April 2009
On heights of algebraic numbers, Algebra / Number Theory / Combinatorics Seminar, Claremont Colleges, March 2009
On Tarski plank problem and its discrete analogues, Analysis Seminar, Claremont Colleges, November 2008
On Siegel's lemma, Algebra / Number Theory / Combinatorics Seminar, Claremont Colleges, September 2008
On distribution of well-rounded sublattices of Z^2, Analysis Seminar, Claremont Colleges, September 2008
Mahler's measure, Lehmer's conjecture, and some connections - II, Analysis Seminar, Claremont Colleges, April 2008
Mahler's measure, Lehmer's conjecture, and some connections - I, Analysis Seminar, Claremont Colleges, February 2008
On zeta function of well-rounded lattices, Analysis Seminar, Claremont Colleges, November 2007
Hilbert's 10-th problem, heights, and search bounds for rational points on varieties, Parts I and II, Algebra / Number Theory / Combinatorics Seminar, Claremont Colleges, September 2007
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, Part I, 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

Other special programs and conferences attended

Arizona Winter School: Special Functions and Transcendence , Tucson, AZ, March 2008
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

Professional activities and service

Co-organizer (with W. K. Chan, R. Schulze-Pillot, J. Vaaler) of a 5-day workshop on Diophantine methods, lattices, and arithmetic theory of quadratic forms, BIRS, Banff, Canada (November 13 - 18, 2011)
Member of the Ph.D. Dissertation Committee for Mark Rothlisberger (University of Texas at Austin, 2010)
Organizer for the Algebra / Number Theory / Combinatorics seminar, Claremont Colleges, 2009-2010
Co-organizer (with M. Beck) of AMS Special Session: Diophantine problems and discrete geometry, AMS Spring Western Section Meeting, Claremont, CA, May 2008
Local organizer of AMS Spring Western Section Meeting, Claremont, CA, May 2008
Referee for Journal of Number Theory, Canadian Mathematical Bulletin, International Journal of Number Theory, Mathematics of Operations Research, Journal of Combinatorial Theory A, Acta Arithmetica, Proceedings of the American Mathematical Society, Advances in Geometry, American Mathematical Monthly, Mathematica Bohemica, Canada Council for the Arts: Killam Program
Reviewer for Mathematical Reviews and Zentralblatt MATH
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

Special Teaching Activities

Instructor and Project Leader for an NSF-funded REU program, Claremont Colleges REU, 2009
Speaker for a GEMS (Gateway to Exploring Mathematical Sciences) event for middle school students, 2009
Co-organizer (with M. O'Neill) of Putnam preparation seminar at Claremont McKenna, 2007, 2008
Co-organizer (with M. O'Neill) of a mathematical problem-solving contest at Claremont McKenna, 2008
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

Courses Taught

Algebraic Number Theory (advanced topics course), Claremont McKenna College, Instructor
Abstract Algebra II: Galois Theory, Claremont McKenna College, Instructor
Abstract Algebra I, Claremont McKenna College, Instructor
Discrete Geometry (special topics course), Claremont McKenna College, Instructor
Linear Algebra, Claremont McKenna College, Instructor
Number Theory, Claremont McKenna College, Instructor
Calculus I and II, Calculus III (Honors), Claremont McKenna College, Instructor
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

Lecture Notes (available on the webpage in PDF format)

Discrete Geometry: lecture notes written for the special topics undergraduate course taught at Claremont McKenna, Fall 2008
Diophantine Approximation and Geometry of Numbers: lecture notes written for the special topics graduate course taught at Texas A&M, Spring 2006

Computing Skills

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