Nantel Bergeron
Full Professor, Department of Mathematics & Statistics
York Research Chair in Applied Algebra
Academic Degrees
PhD, University of California
Postdoctoral Positions

Princeton

Harvard University
Research Interests
Lay Research Summary
My work focuses on solving algebraic problems using combinatorial tools. Specifically, I will investigate new combinatorial problems related to mathematical physics and other areas.
Scientific Research Summary
I work on combinatorial algorithms and special functions, two areas that are vital for our most innovative ventures. This work is motivated in part by a need for better combinatorial algorithms in communication systems and in data analysis. This is well understood by Google, a company that thrives o ...read moren the use of mathematics for all of its activities. For example, the PageRank algorithm of Google is based on the PeronFrobenius theorem (1912) in linear algebra. Accordingly, they hire pure mathematicians to develop their products. In fact, Google in California has hired two of my recent postdocs and one junior coauthor for their combinatorial algorithm skills.
My research program involves studying the deep interactions between Algebra, Combinatorics, Representation Theory, and Algebraic Geometry, with interesting ties to Theoretical Physics and Computer Science. In my studies, I systematically use and develop experimental tools in Computer Algebra. As one of the pioneers in the theory of Combinatorial Hopf Algebras, I have not only made significant breakthroughs, but I have created new classes of problems to be understood in a wide range of areas. To this end, I have developed an extensive international web of collaborators, with whom I am currently advancing on the fundamental questions raised by my program.
I plan to continue developing the foundations of Combinatorial Hopf Algebra theory. This will allow me to find more innovative combinatorial results with greater impacts for science. Certain Combinatorial Hopf Algebras contain special functions of great interest to physics. Some of these special functions encode the physical properties of particle models. Other such functions encode the way the particles interact in the models. A basic task in quantum computing requires designing spin networks allowing perfect quantum state transfer. The combinatorial methods associated to special functions that we are developing have direct applications in the development of quantum computers.
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Publications Link
Select Publications

Combinatorial Hopf algebras and generalized Dehn–Sommerville relations
Journal: Compositio Mathematica
2006

Noncommutative Pieri operators on posets
Journal: Journal of Combinatorial Theory
2000

Lattice diagram polynomials and extended Pieri rules
Journal: Advances in Mathematics
1999

RCgraphs and Schubert polynomials
Journal: Experimental Math
1993

A decomposition of the descent algebra of a finite Coxeter group
Journal: Journal of Algebraic Combinatorics
1992
Honours & Awards
Field Institute Fellow
2012Premier’s Research Excellence Award
20002005Canada Research Chair
20012011York President’s Award for most promising scholar
1996Alfred P. Sloan Doctoral Dissertation Fellowship
198990Thomas Temple Hoopes Prizes at Harvard University for advisory work
1993York Research Chair
2016
Internal Collaborations
JW Darewych
Department of Physics & Astronomy
Faculty of ScienceY Gao
Department of Mathematics & Statistics
Faculty of ScienceM Zabrocki
Department of Mathematics & Statistics
Faculty of Science
Editorial & Review Boards

Canadian Mathematical Bulletin
Role: Editor in Chief
Year: 20062010

International Journal of Combinatorics
Role: Editor
Year: 2008present

Algebra Letters
Role: Editor
Year: 2012present

Journal of Discrete Mathematics
Role: Editor
Year: 2012present

Open Journal of Discrete Mathematics
Role: Editor
Year: 2012present

Canadian Math. Society
Role: Chair of Publication Committee
Year: 201215

NSERC
Role: Committee 1508
Year: 200912

Canadian Math. Society
Role: Board of Directors
Year: 200711

Canadian Math. Scociety
Role: Chair of Scientific Committee
Year: 201618
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