Noncommutative Analysis

Tag: summer projects

Three classification results in the theory of weighted hardy spaces in the ball – summary of summer project

Last month we had the Math Research Week here at the Technion, and I promised in a previous post to update if there would be any interesting results (see that post for background on the problems). Well, there are! I am writing this short post just to update as promised on the interesting results.

The two excellent students that worked with us – Danny Ofek and Gilad Sofer – got some nice results. They almost solved to a large extent the main problems mentioned in my earlier post. See this poster for a concise summary of the main results:

Danny and Gilad summarized their results in the following paper. Just take a look. They have some new results that I thought were true, they have some new results that I didn’t guess were true, and they also have some new and simplified proofs for a couple of known results. Their work fits in the long term research project to discover how the structure of Hilbert function spaces and their multiplier algebras encodes the underlying structures, and especially the geometry of sets in the unit disc or the unit ball. More on that soon!

Summer project 2020 – Hilbert function spaces of analytic functions in a complex variable

In the week of September 6-11 the Math Department at the Technion will again host the “Math Research Week“, or what we refer to as the the “summer projects week”. As in previous years, I will be offering a project, and this year, with the help of Ran Kiri and Satish Pandey, it will be a project on Hilbert function spaces. See here for the abstract. The purpose of this post is to collect my thoughts and my plans for this project.

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The complex matrix cube problem summer project – summary of results

In the previous post I announced the project that I was going to supervise in the Summer Projects in Mathematics week at the Technion. In this post I wish to share what we did and what we found in that week.

I had the privilege to work with two very bright students who have recently finished their undergraduate studies: Mattya Ben-Efraim (from Bar-Ilan University) and Yuval Yifrach (from the Technion). It is remarkable the amount of stuff they learned for this one week project (the basics of C*-algebras and operator spaces), and that they actually helped settle the question that I raised to them.

I learned a lot of things in this project. First, I learned that my conjecture was false! I also learned and re-learned some programming abilities, and I learned something about the subtleties and limitations of numerical experimentation (I also learned something about how to supervise an undergraduate research project, but that’s besides the point right now).

Statement of the problem

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