SCIENTIFIC PROGRAMS AND ACTIVITIES
|December 21, 2014|
For a General Audience:
Beginning with the development of calculus in the 1680s, mathematical analysis treaded on new territory with very insecure footings. In the following century, study of the vibrating string (Fourier series) exposed many problems in the way mathematicians thought of functions, limits and even real numbers. It took about 200 years to realize that a rigorous, non-geometric, approach to the study of functions was necessary, and to figure out how to resolve the difficulties. This resolution led to our modern view of mathematics.
For a Mathematical Audience:
I will discuss how to study commuting sets of operators on Hilbert space which satisfy polynomial relations. Under a natural norm constraint, there is a universal operator algebra that models this. In an effort to classify these algebras up to isomorphism, one must deal with the variety associated to the polynomial relations. Classification up to completely isometric isomorphism is very nice. But the algebraic isomorphism problem raises many difficulties. Ideas from operator theory and algebraic geometry are combined with a function theoretic representation of our algebras as multipliers on a Hilbert space of functions on the variety
Kenneth R. Davidson is a Professor of Pure Mathematics at the University of Waterloo. He did his undergraduate work at Waterloo and received his Ph.D. from the University of California, Berkeley in 1976. From 1976 to 1978, he was a Moore instructor at M.I.T. He joined the faculty at Waterloo in 1978. In 1985, he won the Israel Halperin Prize in operator algebras. He was appointed a Fellow of the Royal Society of Canada in 1992, and a Fellow of the Fields Institute in 2006. From 2001 to 2004, he served as Director of the Fields Institute. In 2007 he became University Professor at the University of Waterloo. Professor Davidson's research interests include operator algebras and functional analysis, and their applications to other areas of mathematics. He has published over 120 scientific papers and 4 monographs, and has supervised 8 Ph.D. students and 20 postdoctoral fellows.