• Math845 – Algebra Two.

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 (all here at UD, unless otherwise stated):

• 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)
• 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 Arkansas Rich Mountain)
• Paul Hearding (completed May 25)
• Ali Ibrahim A Asiri (departed Flinders University of South Australia, Sep 25)
• Stephen Brittain (current)
• Randon Weaver (current)