Lenny's Page

I am now on the faculty in the Mathematics Department at Claremont McKenna College. This page is no longer maintained - please visit my new page.

I am a Visiting Assistant Professor at the Mathematics Department of Texas A&M University. I received my Ph.D. in 2004 from the University of Texas at Austin (the irony!) under Professor J. D. Vaaler. My area of research is Number Theory and Discrete Geometry, more specifically my interests are in

• 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 (pdf)
2. Small zeros of quadratic forms with linear conditions, Journal of Number Theory, vol. 108 no. 1 (2004), pg. 29-43 (pdf)
3. (with Matthias Beck, Beifang Chen, Christian Haase, Allen Knutson, Bruce Reznick, Sinai Robins, and Achill Schuermann) Problems from the Cottonwood Room, Contemporary Mathematics 374 (2005), 179-191 (Proceedings of the Summer AMS/MAA/SIAM Research Conference on Integer Points in Polyhedra, July 13 - July 17, 2003 in Snowbird, Utah) (pdf - my section of this paper: Lattice points in homogeneously expanding compact domains) - I have Erdös number 2 thanks to this paper!
   
4. Integral points of small height outside of a hypersurface, Monatshefte für Mathematik, vol. 147 no. 1 (2006), pg. 25-41 (pdf)
5. Siegel's lemma with additional conditions, Journal of Number Theory, vol. 120 no. 1 (2006), pg. 13-25 (pdf)
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 (.pdf)
7. On effective Witt decomposition and Cartan-Dieudonné theorem, to appear in Canadian Journal of Mathematics (.pdf)
8. Search bounds for zeros of polynomials over the algebraic closure of Q, to appear in Rocky Mountain Journal of Mathematics (.pdf)
   
9. Small zeros of quadratic forms over the algebraic closure of Q, to appear in International Journal of Number Theory (.pdf)
10. On distribution of well-rounded sublattices of Z^2, preprint (.pdf)
11. On similarity classes of well-rounded sublattices of Z^2, preprint (.pdf)
    

1. On distribution of integral well-rounded lattices in dimension two, Illinois Number Theory Fest, May 2007 (.pdf)
   
2. Quadratic forms and height functions, Colloquium of the Graduiertenkolleg, University of Göttingen, June 2006 (.pdf)
   
3. Simultaneous Diophantine approximations and a conjecture of Minkowski (expository talk), Introduction to Mathematical Research seminar series, University of Texas at Austin, March 2006 (.pdf)
   
4. 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 (.pdf)
   
5. Frobenius problem and the covering radius of a lattice, West Coast Number Theory, Pacific Grove, CA, December 2005 (.pdf, data)
   
6. Some effective Diophantine results over the algebraic closure of Q, XXIVth Journées Arithmétiques, Marseilles, France, July 2005 (.pdf)
   
7. Effective decompositions of quadratic spaces, ArithmeTexas, College Station, TX, April 2005 (.pdf)
   
8. Counting lattice points in admissible adelic sets, MNTCG2, Urbana-Champaign, IL, February 2005 (.pdf)
   
9. Heights and Diophantine problems, September 2004, Colloquium, Rice University  (.pdf)
10. Siegel's lemma with additional conditions, June 2004, CNTA8 (.pdf)
11. Integral points of small height outside of a hypersurface, May 2004, Illinois Number Theory Conference (.pdf)
12. Small zeros of quadratic forms with linear conditions, June 2003, Mahler's Measure of Polynomials (.pdf)
    

• Diophantine approximations and geometry of numbers: lecture notes for a graduate topics course I taught in the Spring 2006 semester (.pdf)
  

• Spring 2007:     M222 (section 200) - Linear Algebra
  
• Fall 2006:          M171 (sections 501 and 504) - Calculus I (for math and science majors)
  
• Spring 2006:     M662 (section 602) - Diophantine Approximations and Geometry of Numbers
  
• Fall 2005:          M152H (sections 201 - 202) - Calculus II (Honors)
  
• Fall 2005:          M304 (sections 502 - 503) - Linear Algebra
  
• Summer 2005:  M662 (section 100) - REU/VIGRE Course: Algebraic Methods in Computational Biology
  
• Spring 2005:     M601 (section 602) - Methods of Applied Mathematics I
  
• Fall 2004:          M601 (section 602) - Methods of Applied Mathematics I

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