Conference on Multivariable Operator Theory and Function Spaces in Several Variables

该奖项将为10名美国研究人员提供旅费支持，以参加将于2021年8月1日至6日在墨西哥瓦哈卡州的BIRS-CMO设施举行的题为“多变量算子理论和多变量函数空间”的会议。这次会议的一个新颖之处在于，它将召集一组初级和高级研究人员，他们将共同努力解决该领域的一个主要问题。通过优先考虑早期职业研究人员的参与，这项资助将有助于美国劳动力的发展。会议的科学焦点是算子理论和函数空间，两者都是更广泛的数学分析领域的一部分。为了描述要研究的具体问题，请注意1963年Ando的一个定理：如果T是Hilbert空间上的一对交换收缩，那么，对于任何多项式p， p(T)的范数最多是p在双盘上的最大模。这对于3个或更多的交换收缩是不成立的，但是对于一个常数，这个不等式是否仍然成立是未知的。事实证明，这是发展从两个到三个或更多变量的多变量算子理论的巨大障碍。这次会议的主要目的是在解决这个问题方面取得进展，并为一些特殊情况找到明确的答案。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，认为值得支持。

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.