David Wehlau

Professor
Department of Mathematics and Statistics
Queen's University

Address:
Dept. of Mathematics & Statistics
Queen's University
Kingston, Ontario
Canada K7L 3N6
Location: 503 Jeffery Hall
Telephone:
office: (613) 533-2389
fax: (613) 533-2964
Email:
wehlau@rmc.ca
and wehlau@mast.queensu.ca

Mathematical Myth:

Contrary to a widely held myth, the loneliest number is, in fact, an irrational number between 7 and 8.

Publications:

Click here for a list of my published research

Current Graduate Students

I currently have four graduate students, all co-supervised. Yinglin Wu is finishing his Ph.D. on p-groups with a polynomial ring of invariants over finite fields of characteristic p. Asia Mathews started her Ph.D. studies on toric varieties and has also become interested in university mathematics education. Philippe Depass' Master's involves studying number theory and encryption. Razan Al-Nakhl has just started her Master's studies in algebra and information theory.

Students Who Recently Graduated

Students who have recently completed graduate degrees in invariant theory include Chester Weatherby, Emilie Dufresne, Jianjun Chuai, Chris Brav, and David Giordano. Jianjun finished his Ph.D. in August 2003 and now is an postdoctoral fellow in St. John's. Chester(2005), Emilie(2004), Chris(2003), David(2001) and Letitia(2006) all completed Master's degrees. Emilie and Chris all went on to complete Ph.D. degrees at Queens's in 2008. Chester is completing his Ph.D. at Queen's in number theory. Letitia is working on her Ph.D at the University of Western Ontario. David left after getting his Master's and is now doing financial mathematics for TD Canada Trust in Toronto.

I have also had students recently 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 working on his Ph.D. at the University of Guelph. Second Lieutenant Joe Oldford completed his Master's at RMC in 2007 on Secret Key Distribution and Encryption. He is now posted to Canadian Forces Base North Bay.

Recent Conferences:

I have co-organized two major conferences on algebraic groups in the past few years.

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.

Public Lecture:

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 poster 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 ".

Research Interests:

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.)

Previous Experience

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 Schwarz .

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 Eddy Campbell, 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 acting President of Memorial. 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 regularly work with are Mike Roth, Greg Smith, and Tony Geramita. Another one of my regular 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 characteristic.

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 theory. Galois geometries are geometries where there are only a finite number of points, lines, planes, etc. Most of this work is with my collaborators Aiden Bruen, Lucien Haddad and Claude Tardif . 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 .

Other duties

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.

Personal Info

My wife and I have three cats. We live in Kingston in the former Pittsburg Township about 10 kilometers from RMC. On December 6, 2008 we had our first child, Megan. Here are some photos of my family in which Megan features prominantly.