- Math210: Discrete Mathematics I
- 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 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, 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)
- Emily Bergman (completed Jul 20, now at NSA)
- Bradley Fain (completed Jul 21, now at Colorado State)
- Paul Hearding (current)
- Li-An Chen (current)
- Kamal Joshi (current)
- Stephen Brittain (current)