Research Interests

Finite Geometries, combinatorics, and other topics in discrete mathematics and geometry. 

 Publications 

• With E. Diaz. Translation planes admitting a linear Abelian group of order (q+1)^2. Preprint pdf.
• With F. Lazebnik & K. Mellinger. On the number of k-gons in finite projective planes. Preprint pdf.
• Geometric structures arising from generalized j-planes. To appear in  Note di Matematica vol. 29, n. 2 (2009). pdf.
• Generalized j-planes. To appear in  Note di Matematica vol. 29 n. 2 (2009). pdf.
• With N. L. Johnson. Symplectic spreads and symplectically paired spreads. Note di Matematica vol. 26, n. 2 (2006). 119-134. pdf
• With N. L. Johnson & F. W. Wilke. j,k-planes of order 4^3. Innovations in Incidence Geometry (2) 2006. 1-34. pdf.

• (In progress) with E. Diaz. Translation planes admitting a group of order (q+1)^2.
• (In progress) with F. Lazebnik & K. Mellinger. Embeddings of graphs in finite planes.
• (In progress) with L. Cusick. Abelian groups that are derangements of the n-cube. 
• (In progress... for ever). Brown's theorem.
• (In progress... for ever). Polynomial invariants for spreads and regular parallelisms of deficiency one of PG(3,q).

Talks (a few of them)

• Embeddings of graphs in finite planes: NormFest. University of Texas at San Antonio. March 27, 2009. pdf
• Flat flocks and generalized j-planes: AMS/MAA joint meeting in Washington DC. January 06, 2009. pdf
• More Questions Than Answers. Mathematics Department Seminar. California State University, Fresno. October 30, 2008.
• An invariant for spreads of PG(3,q): Mathematics Department Seminar. California State University, Fresno. February 28, 2009. pdf
• Parallelisms of PG(3,q): Mathematics Department Seminar. California State University, Fresno. February 21, 2008. pdf
• Symplectic geometry over finite fields II: Mathematics Department Seminar. California State University, Fresno. October 25, 2007. pdf
• Symplectic geometry over finite fields I: Mathematics Department Seminar. California State University, Fresno. October 18, 2007. pdf
• Symplectic translation planes II: Rocky Mountain Algebraic Combinatorics Seminar. CSU, Fort Collins. February 23, 2007. pdf
• Symplectic translation planes I: Discrete Mathematics Seminar. University of Colorado Denver. February 19, 2007. pdf
• An algebraic combinatorial view to knots and links: Discrete Mathematics Seminar. University of Colorado Denver. January 29, 2007. pdf
• jj...j-planes: Rocky Mountain Algebraic Combinatorics Seminar. CSU, Fort Collins. September 29, 2006. pdf
• M.C. Escher: GAUSS, University of Iowa. March 23, 2006. pdf (heavy!).
• Flat flocks: Finite Geometries Seminar, University of Colorado, Denver. February 13, 2006. pdf
• jj...j-planes: Discrete Mathematics Seminar, University of Colorado, Denver. February 13, 2006. pdf
• A polynomial invariant for spreads: Rocky Mountain Algebraic Combinatorics Seminar, CSU, Fort Collins. February 10, 2006. pdf
• The power of counting: Euler's characteristic: Cornell College. A short version of "COUNT on me, I'll be DISCRETE". January 17, 2006.
• j,k-planes of order 4^3: AMS/MAA joint meeting in San Antonio. January 14, 2006. pdf
• COUNT on me, I'll be DISCRETE: Graduate And Undergraduate Students Seminar (GAUSS), University of Iowa. October 5, 2005. pdf

My Erdös number is less or equal to 4.

- Cameron, P. J.; Erdös, P. On the number of sets of integers with various properties. Number theory (Banff, AB, 1988), 61--79, de Gruyter, Berlin, 1990.

- Cameron, P. J.; Thas, J. A.; Payne, S. E. Polarities of generalized hexagons and perfect codes. Geometriae Dedicata 5 (1976), no. 4, 525--528.

- Gevaert, H.; Johnson, N. L.; Thas, J. A. Spreads covered by reguli. Simon Stevin 62 (1988), no. 1, 51--62.

- Johnson, N. L.; Vega, O. Symplectic spreads and symplectically paired spreads. Note di Matematica vol. 26, n. 2 (2006). 119-134.

My math genealogy is here

Back to the Main Page