Department of Mathematics
Dept. of Mathematics & Statistics
Canada K7L 3N6
Location: 503 Jeffery Hall
office: (613) 533-2389
fax: (613) 533-2964
Contrary to a widely held myth,
the loneliest number is, in fact, an irrational number between 7 and 8.
Click here for a list of my
Current Graduate Students
I currently have two graduate students, both co-supervised.
Asia Mathews started her Ph.D. studies on toric
varieties and has also become interested in university mathematics education.
The births of her two lovely children have briefly interupted her studies but she juggles her
home and research duties expertly and will finish her Ph.D. soon.
Sean Zimmerman is a Master's student studying graph theory. He started in September 2012.
Students who have completed
graduate degrees in invariant theory include
Jianjun Chuai, Chris Brav,
and Catherine Chambers.
Yinglin finished his Ph.D. in September 2009 and went on to continue his studies
in biostatistics at the University of Waterloo.
Emilie completed her Ph.D. in August 2008. After a Post Doctoral position
at the University of Heidelberg she is now working on her Habilitation degree at the University of Basel in Switzerland.
Jianjun finished his Ph.D. in
August 2003 and now is at the University of New Brunswick in Fredericton, NB.
Emilie(2004), Chris(2003), David(2001) and Catherine (1998)
all completed Master's degrees.
Emilie, Chris and Chester went on to complete Ph.D. degrees at Queens'.
Letitia completed a Ph.D. at the University of Western Ontario and now does
financial mathematics for TD Canada Trust in Toronto.
David left after getting his Master's
and is now a Senior Manager doing Quantitative Analytics
at TD Canada Trust in Toronto.
I have also had students graduate in fields other than
invariant theory. Sebi Cioaba
completed his Ph.D. on Expander Graphs in 2006 and has a tenure track position
at the University of Delaware. In 2002 Jenny Vandergraaf (now
Jenny Waite) finished her Master's on Linefree subsets in Projective Space
over the field of order 2. She is now a database administrator for the
United Way in Brockville, Ontario. Daniel Bruce completed his Master's in
graph theory in 2007 and is now a Software Developer at Desire2Learn
in Kitchener, Ontario.
Second Lieutenant Joe Oldford completed his Master's at RMC in
2007 on Secret Key Distribution and Encryption. He is now a captain posted to Canadian
Forces Base North Bay.
Razan Al-Nakhl completed her Master's degree in 2011 studying information theory.
In June 2010 Eddy Campbell, Jianjun Chuai and I co-organized a special
Group Actions and Their Invariants
at the CMS summer meeting in Fredericton New Brunswick.
Click here for a list of speakers and slides from their talks.
I have co-organized two major conferences on algebraic groups.
In July 2006, along with Eddy Campbell, Loek Helminck and Hanspeter Kraft, I organized a conference
Symmetry and Spaces; A Conference on the Occasion of Gerry Schwarz's 60th Birthday
at the Fields Institute.
In April 2002, Eddy Cambell and I co-organized an
invariant theory workshop & conference
in connection with the Centre de Recherches Mathématiques'
theme year on
Groups and Geometry.
I was awarded the 2012 Cowan Prize for Excellence in Research. This is RMC's top reseach prize and the winner gives a public lecture in celebration of the award.
Here is the poster advertising my talk, entitled "Quantum Cryptography: An Unbreakable Cipher".
In May 2002 I was awarded the 2001-2002 RMC
Class of 1965 Teaching Excellence Award
. One of the honours associated with this award is that I was asked
to give a public lecture. Here you can see the beautiful
RMC produced advertising the leture. You
can read my notes and see the slides from the lecture entitled
"Soldiers, Spies, Crooks: Their Ciphers and Secret Codes
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
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.)
I received my Honours Bachelor of Science degree from the
University of Western Ontario
. My degree is in their
Scholars Electives program
specializing equally in Mathematics
and Computer Science
I received both my Master of Arts and my Ph.D. from the
Department of Mathematics
at Brandeis University
. My Master's was in Number Theory with
Dr. Paul Monsky
as my supervisor. My Ph.D. thesis was on Invariant Theory and my supervisor
was Dr. Gerald
After leaving Brandeis, I was an Assistant Professor at the
University of Toronto
in the Department of Mathematics
for the period 1988-1992.
My Current Work
I have been in Kingston since the fall of 1992. I work regularly
on joint projects with
Ian Hughes who are both members of the Queen's math department.
In 2004 Eddy moved to Memorial
University of Newfoundland where he is the Vice President Academic and
the Pro Vice Chancellor. (I always suspected that Eddy was in favour of
vice but who knew he could parlay it into a salary?)
He is now President of the University of New Brunswick.
From 1995 until August
1999 Jim Shank
was also at Queen's. In August
1999, Jim left us for the greener pastures (and better choir) at the
University of Kent
at Canterbury, England. Jim and I are still working together but we
now usually use email to conduct our discussions.
There are a number of
algebraists at Queen's.
Among those I work with are
and Tony Geramita.
Another one of my
collaborators on invariant theory is Gregor Kemper.
Eddy Campbell, Ian Hughes and Jim Shank are principally interested in finite groups which
are of course much easier than infinite ones (well at least much smaller than
infinite ones) but usually they make the problem hard by working in positive
The algebraists at Queen's have a whole lot of fun doing research and
attending our various seminars (including the
algebraic geometry seminar).
I am also doing research in the area of Galois geometries and graph
Galois geometries are geometries
where there are only a finite number of points, lines, planes, etc. Most
of this work is with my collaborators
My research on Galois geometries is concerned with finding maximal line
free subsets in geometries over finite fields. I am also studying blocking
sets. These are sets which meet every subspace of a given dimension.
The study of blocking sets and line free sets yields methods to construct
new encryption codes and/or shows that various desired codes cannot exist.
In graph theory I am studying properties of colourings of hypergraphs.
I am a professor in the
Department of Mathematics
at the Royal Military College of Canada
(which is a university even though the name makes it sound a little like
a college). I do all my undergraduate teaching at RMC. Here
I am lecturing
on a day when I returned the exam. Up until the spring of 2000, I was the
coach of the
RMC varsity badminton team
. You can read all about my activities at RMC on my
internal RMC homepage
or on my
public RMC homepage
I play indoor (in the winter) and outdoor (in the summer) soccer regularly
at lunch at Queen's. I
play with the "nooners
", so-called since we play beginning at 11:00 or 11:30 in the winter (which
really means 11:15 or 11:45) and 12:30 in the summer.
My principal duty when we play at Queen's used
to be humiliating the former Associate Dean of Arts and Science
Eddy, Canadian Tire, Campbell. Since Eddy moved to Newfoundland, I
have to content myself with scoring the occasional goal.
My wife and I have three cats. We live in
former Pittsburg Township
about 10 kilometers from RMC.
On December 6, 2008 we had our first child, Megan. Here are some
of my family in which Megan features prominantly.
This page is currently under deconstruction. Last deconstructed
on November 6, 2012.