• Math451 – Abstract Algebra.

Research Interests:

• • Finite fields and applications.
  • Polynomials over finite fields, particularly their roles in projective geometry, information security and combinatorics.
  • Construction of cryptographically useful functions such as APN functions, planar functions, and PPs with low differential uniformity.
  • Construction and classification of Cartesian groups, quasifields and semifields.
  • Automorphism groups of combinatorial and algebraic objects, and the interrelated problems of isotopy of algebraic objects and isomorphism of projective planes.
  • Projective planes, especially planes of small order, the Prime Power Conjecture and the Prime = Desargues Conjecture.

You can find a publication list here.

The following students have so far had the extreme wisdom (i.e. been foolish enough) to work with me on their PhDs:

• Todd Gutekunst (completed May 08, now at King’s College)
• Pamela Kosick (completed Dec 09, now at Stockton University)
• Chris Castillo (completed May 15, now at Cecil College)
• Chris Ulicny (departed with Masters, May 15)
• Patrick Cesarz (completed Oct 19, now at University of Wyoming)
• Emily Bergman (completed Jul 20, now at NSA)
• Bradley Fain (completed Jul 21)
• Li-An Chen (completed Apr 23, now at Boise State University)
• Kamal Joshi (completed Sep 23, now at University of Delaware)
• Paul Hearding (current)
• Stephen Brittain (current)
• Randon Weaver (current)
• Ali Ibrahim A Asiri (current)