معرفی
Professor Peter J. Dukes holds a faculty position in the Department of Mathematics and Statistics at the University of Victoria. His research focuses on combinatorics, particularly applying algebraic and analytic methods to combinatorial problems. He has held positions including postdoctoral fellowships at Arizona State University and the University of Toronto. Dukes teaches advanced courses such as MATH 427 (Combinatorial Designs) and MATH 529 (Topics in Discrete Mathematics). His work spans graph theory, coding theory, and quasirandomness, with recent publications addressing graph decomposition, matrix balancing, and permutation patterns. He actively participates in academic conferences and organizes sessions on combinatorial design theory. His teaching philosophy emphasizes problem-solving and the appreciation of mathematical beauty, supported by resources like lecture notes for MATH 413 (applied algebra). Dukes also engages in outreach through activities like the UVic Math Competition and triangle decomposition games.
Education:
- B.Sc. Mathematics, University of Victoria, 1997
- M.Sc. Mathematics, University of Toronto, 1998
- Ph.D. Mathematics, California Institute of Technology (Caltech), 2003
Research Interests: Combinatorics, algebraic methods in combinatorics, extremal graph theory, quasirandom structures, and applications to coding theory. His work often explores the intersection of discrete mathematics with algebraic techniques, such as permutation balancing and matrix decomposition problems.
