Noncommutative Analysis

Month: April, 2020

The 48th Canadian Operator Symposium will be held online

I got an email announcing that COSY 2020 will be held online. This is very nice news! The organizers say that

We would like to announce that the 48th Canadian Operator Symposium will be held online May 25 to May 29.  Since many of the early summer Operator Algebra conferences have been cancelled and since we have the support and structural capabilities of the Fields Institute, our hope is to make the best of the current situation and provide a conference experience to the operator algebra community where researchers can present their research and can collaborate and socialize with others.

All talks will be given with Zoom (there are plenary speakers and there will be parallel session of contributed talks), and there will be “lunches” and “work rooms”. They say more details will be in the site soon. I plan to check it out.

Dilations of q-commuting unitaries

Malte Gerhold and I just have just uploaded a revision of our paper “Dilations of q-commuting unitaries” to the arxiv. This paper has been recently accepted to appear in IMRN, and was previously rejected by CMP, so we have four anonymous referees and two handling editors to be thankful to for various corrections and suggested improvements (though, as you may understand, one editor and two referees have reached quite a wrong conclusion regarding our beautiful paper :-).

This is a quite short paper (200 full pages shorter than the paper I recently announced), which tells a simple and interesting story: we find that optimal constant c_\theta, such that every pair of unitaries u,v satisfying the q-commutation relation

vu = e^{i\theta} uv

dilates to a pair of commuting normal operators with norm less than or equal to c_\theta (this problems is related to the “complex matrix cube problem” that we considered in the summer project half year ago and the one before). We provide a full solution. There are a few ramifications of this idea, as well as surprising connections and applications, so I invite you to check out the nice little introduction.