Brett Stevens - Research

I am interested in combinatorics and mathematical biology. Aspects of combinatorics that interest me include combinatorial design theory, coding theory, extremal set theory, randomized search algorithms for combinatorial structures. Topics in biology that interest me include evolution, genetics, sexual selection and the evolution of sex.

I am currently a PIMS postdoctoral fellow in the Department of Mathematics and Statistics at Simon Fraser University working with Prof. Brian Alspach, Prof. Kathy Heinrich and Prof. Pavol Hell. My current research is the continuing investigation transversal packings from my thesis and finding good randomized search method for covers and packings. I am interested in finding a particular class of resolvable pairwise balanced designs and decompositions of graphs into partial 1-factors. I am also interested in extending standard genetic algorithms to include variable genome sizes. I am continuing my investigation into the evolution of sexual reproduction which is joint work with Prof. David Houle .

My thesis Transversal Covers and Packings was done in the Mathematics Department at the University of Toronto under the supervision of Prof. Eric Mendelsohn. In the thesis I develop recursive and non recursive constructions, upper and lower bounds for both transversal packings. I obtained several optimality results. I also solved the Anti-Oberwolfach problem. I completed my masters work studying the evolution of sex with Prof. David Houle .

During the 1992-1993 school year I took a break from institutional education and worked on an American Nuclear Society exchange program with Electricité de France investigating potential nuclear accidents involving heterogeneous boron concentrations in pressurized water reactors. Later that year I worked for a toy factory in London. In the last half of the year I worked with Dr. Douglas Bishop in the Radiation Oncology Department at the University of Chicago maintaining databases and developing computer imaging software. In the summer of 1993 I worked for Jeanne Altmann in the Department of Ecology and Evolution maintaining her databases and compiling data. From 1988 to 1992 I completed my honors B.A. in mathematics from the University of Chicago, working several summers for Dr. Teng-Lek Khoo in the Nuclear Structure Research Group at Argonne National Labs. There I modified nuclear cascade simulations and programmed random number generators.

Publications

  1. BRETT STEVENS and ERIC MENDELSOHN, New Recursive Methods for Transversal Covers, (1997), to appear in Journal of Combinatorial Designs .
  2. BRETT STEVENS, LUCIA MOURA and ERIC MENDELSOHN, Lower bounds for transversal covers, (1997), to appear in Designs, Codes and Cryptography.
  3. Mathematical Poem, in Dec. 1992 issue of Harper's and Christmas 1991 issue of New Scientist .

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Web Publications

  1. BRETT STEVENS , "Introduction to Combinatorial Block Designs"
  2. BRETT STEVENS, "Constructions of Pan-Cyclic 2-factorizations in Complete Graphs"

Academic Information


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