Conference on Multivariable Operator Theory and Function Spaces in Several Variables

This award will provide travel support for 10 US based researchers to attend the conference entitled "Multivariable operator theory and function spaces in several variables" that will be held August 1-6, 2021, at the BIRS-CMO facility in Oaxaca, Mexico. A novel aspect of the conference is that it will convene a group of both junior and senior researchers who will work together on solving a major problem in the field.

By prioritising the participation of early career researchers, this grant will contribute to US workforce development.

The scientific focus of the conference is Operator Theory and Function Spaces, both part of the broader area of Mathematical Analysis. To describe the specific problem to be investigated, note that a theorem of Ando from 1963 says that if T is a pair of commuting contractions on a Hilbert space, then, for any polynomial p, the norm of p(T) is at most the maximum modulus of p on the bidisk.

This fails for 3 or more commuting contractions, but it is unknown whether the inequality still holds with a constant or not. This has proved to be a huge stumbling block in developing multivariable operator theory from two to three or more variables. The principal aim of this conference is to make progress on resolving this question and to find definitive answers for some special cases. The conference website is https://www.birs.ca/cmo.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.