Noncommutative Analysis

Category: Talks

Around and under my talk at Fields

This week I am attending a Workshop on Developments and Technical Aspects of Free Noncommutative Functions at the Fields Institute in Toronto. Since I plan to give a chalk-talk, I cannot post my slides online (and I cannot prepare for my talk by preparing slides), so I will write here what some ideas around what I want to say in my talk, and also some ramblings I won’t have time to say in my talk.

[Several years ago I went to a conference in China and came back with the insight that in international conferences I should give a computer presentation and not a blackboard talk, because then people who cannot understand my accent can at least read the slides. It’s been almost six years since then and indeed I gave only beamer-talks since. My English has not improved over this period, I think, but I have several reasons for allowing myself to give an old fashioned lecture – the main ones are the nature of the workshop, the nature of the audience and the kind of things I have to say]. 

In the workshop Guy Salomon, Eli Shamovich and I will give a series of talks on our two papers (one and two). These two papers have a lot of small auxiliary results, which in usual conference talk we don’t get the chance to speak about. This workshop is a wonderful opportunity for us to highlight some of these results and the ideas behind them, which we feel might be somewhat buried in our paper and have gone unnoticed. 

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The complex matrix cube problem (in “Summer Projects in Mathematics at the Technion”)

Next week I will participate as a mentor in the Technion’s Summer Projects in Mathematics. The project I offered is called “Numerical explorations of open problems from operator theory”, and it suggests three open problems in operator theory where theoretical progress seems to be stuck, and for which I believe that some computer experiments can help us get a feeling of what is going on. I also hope that thinking seriously about designing experiments can help us to understand some general facets of the theory.

I have been in contact with the students in the last few weeks and we decided to concentrate on “the matrix cube problem”. On Sunday, when the week begins, I will need to present the background to the project to all participants of this week, and I have seven minutes (!!) for this. As everybody knows, the shorter the presentation, the harder the task is, and the more preparation and thought it requires. So I will take use this blog to practice my little talk.

Introduction to the matrix cube problem

This project is in the theory of operator spaces. My purpose is to give you some kind of flavour of what the theory is about, and what we will do this week to contribute to our understanding of this theory.

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Souvenirs from Amsterdam

(I am writing a post on hot trends in mathematics in the midst of war, completely ignoring it. This seems like the wrong thing to do, but my urge to write has overcome me. To any reader of this blog: I wish you a peaceful night, wherever you are).

Last week I returned from the yearly “International Workshop on Operator Theory and Applications”, IWOTA 2014 for short (see the previous post for the topic of my own talk, or this link for the slides).

This conference was very broad (and IWOTA always is). One nice thing about broad conferences is that you are able sometimes to identify a growing trend. In this talk I got particularly excited by a series of talks on “noncommutative function theory” or “free analysis”. There was a special session dedicated to this topic, but I was mostly inspired by a semi-plenary talk by Jim Agler, and also by two interesting talks by Joe Ball and Spela Spenko. I also attended nice talks related to this subject by Victor Vinnikov, Dmitry Kalyuhzni-Verbovetskyi, Baruch Solel, Igor Klep and Bill Helton. This topic has attracted the attention of many operator theorists, for its applications as well as for its inherent beauty, and seems to be accelerating in the last several years; I will only try to give a taste of some neat things that are going on, by telling you about Agler’s talk. What I will not be able to do is to convey Agler’s intense and unique mathematical charisma.

Here is the program of the conference, so you can check out other things that were going on there.

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Souvenirs from the Black Forest

Last week I attended a workshop titled “Hilbert modules and complex geometry” in MFO (Oberwolfach). In this post I wish to tell about some interesting things that I have learned. There were many great talks to choose from. Below is a sample, in short form, with links.

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The remarkable Hilbert space H^2 (part III – three open problems)

This is the last in the series of three posts on the d–shift space, which accompany/replace the colloquium talk I was supposed to give. The first two parts are available here and here. In this post I will discuss three open problems that I have been thinking about, which are formulated within the setting of H^2_d.

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