Research Interests

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

 Publications 

• With L. Cusick. Finite groups of derangements on the n-cube II. The Electronic Journal of Combinatorics 18(1) #196. 2011  pdf.
• With E. Diaz. Translation planes admitting a linear Abelian group of order (q+1)^2. Note di Matematica 29, suppl. n. 1, 59 - 68, 2009. pdf.
• With F. Lazebnik & K. Mellinger. On the number of k-gons in finite projective planes. Note di Matematica 29, suppl. n. 1, 135 - 152, 2009. pdf.
• Geometric structures arising from generalized j-planes. Note di Matematica 29, n. 2, 2009, 1–18. pdf.
• Generalized j-planes. Note di Matematica 29, n. 2, 2009, 145–166. 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.

• (Submitted) With I. Birnbaum. Various Results on The Well-Covered Dimension of a Graph. (available at ArXiv).
• (To be submitted soon) With V. Jha & N. L. Johnson. Large autotopism groups and flat flocks.
• (In progress) With F. Lazebnik & K. Mellinger. Embeddings of Graphs in Projective Spaces.
• (In progress) With W. Cherowitzo, V. Jha & N. L. Johnson. A Note on Doubly-Transitive alpha-flocks.
• (Stalled) with E. Diaz. Translation planes admitting a group of order (q+1)^2.
• (Stalled). Polynomial invariants for spreads and regular parallelisms of deficiency one of PG(3,q).

• With T. Forgacs. Analysis and Algebra. ISBN: 978-1-60927-756-7. 2012.
• With R. Amarasinghe, L. Burger, M. Nogin, & A. Tuska. Exploring Mathematics: Investigations for Elementary School Teachers. ISBN: 978-1-60927-063-6. 2012.
• With R. Amarasinghe & K. Premadasa. Advanced Algebra for Teachers. ISBN: 978-1-60927-144-2. 2012.
• With M. Cordero & A. Montinaro, Editors. Proceedings of NormFest. ISSN: 1123-2536. e-ISSN: 1590-0932. 2009.

Talks (a few of them)

• Embeddings of graphs in finite projective planes: Mathematics Department Seminar. California State University, Fresno. May 4, 2012. pdf
• Autotopism Groups and jj...j-planes: AMS/MAA joint meeting in Boston, MA. January 05, 2012. pdf
• Autotopism Groups in Translation Planes: Mathematics Department Seminar. California State University, Fresno. October 18, 2011. pdf
• The Math of Sudoku II: College of Science and Mathematics Centennial Celebration. California State University, Fresno. May 13, 2011. pdf
• The Math of Sudoku: Mathematics Department Colloquium. California State University, Fresno. March 25, 2011. pdf
• Groups of Derangements of the n-cube: AMS Spring Central Sectional Meeting. Iowa City, IA. March 20, 2011. pdf
• Clean Rings: Mathematics Department Seminar. California State University, Fresno. November 23, 2010. pdf
• The Well-Covered Dimension of a Graph: Mathematics Department Seminar. California State University, Fresno. March 10, 2010. pdf
• Translation planes admitting a linear Abelian group of order (q + 1)^2: AMS/MAA Joint Meeting. San Francisco. January 13, 2010. pdf
• Embeddings of k-gons and graphs in finite planes: 22nd British Combinatorial Conference. University of St Andrews, Scotland. July 7, 2009.
• Embeddings of graphs in finite planes: NormFest. University of Texas at San Antonio. March 27, 2009. 
• Classifying translation planes by studying their groups of symmetries: Mathematics Department Seminar. California State University, Fresno. March 19, 2009.
• 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 3.

- Erdös, P.; Füredi, Z. Families of finite sets in which no set is covered by the union of two others. J. Combin. Theory Ser. A 33 (1982), no. 2, 158–166. .

- Lazebnik, F.; Füredi, Z. Graphs of prescribed girth and bi-degree. J. Combin. Theory Ser. B 64 (1995), no. 2, 228–239. .

- Lazebnik, F.; Mellinger, K.; Vega, O. On the number of k-gons in finite projective planes. Note di Matematica 29, suppl. n. 1, 135 - 152, 2009.

My math genealogy is here

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