Degrees and Honours
B.Sc. (University of Western Ontario)
M.A. (Brandeis University)
Ph.D. (Brandeis University)
I am interested in algebraic rings of invariants. These are rings formed by polynomials which have enough symmetry to be left unchanged under the action of some (algebraic) group. One of my main interests is in obtaining degree bounds for homogeneous minimal generating invariants. Such bounds give an algorithm for finding rings of invariants. Here are some conjectures I am interested in proving (or disproving).
I also study the interconnections between various conditions which guarantee that the ring of invariants are well-behaved. In particular, I am interested in the Popov (or Russian) conjecture. I have worked on this conjecture for quite a while and have proved it for some special cases including for connected abelian groups (tori).
I am also interested in complete caps in finite projective spaces, especially over the binary field. A cap is a set of points with no three points lying on the same line. A cap is complete if adding any another point to it causes it to have three collinear points. Complete caps are closely connected to certain important error correcting codes.
I am also interested in cryptography, both modern public key and other encryption systems and historic cryptography and cryptoanalysis. In the past I did some work for a Calgary company Non-Elephant Encryption . (There is a long story behind the name of the company.)