What are you working on?

jsalvatier

Whpearson recently mentioned that people in some other online communities frequently ask "what are you working on?". I personally love asking and answering this question. I made sure to ask it at the Seattle meetup. However, I don't often see it asked here in the comments, so I will ask it:

What are you working on?

Here are some guidelines

Focus on projects that you have recently made progress on, not projects that you're thinking about doing but haven't started, those are for a different thread.
Why this project and not others? Mention reasons why you're doing the project and/or why others should contribute to your project (if applicable).
Talk about your goals for the project.
Any kind of project is fair game: personal improvement, research project, art project, whatever.
Link to your work if it's linkable

What are you working on?

Here are some guidelines

Focus on projects that you have recently made progress on, not projects that you're thinking about doing but haven't started, those are for a different thread.
Why this project and not others? Mention reasons why you're doing the project and/or why others should contribute to your project (if applicable).
Talk about your goals for the project.
Any kind of project is fair game: personal improvement, research project, art project, whatever.
Link to your work if it's linkable

Out of idle curiosity (I haven't studied any proof of the Jordan-Schur theorem), are you doing that by tuning up the existing proofs of best bounds through more careful analysis, by replacing relatively large chunks of those proofs by new arguments, or by employing an altogether new proof?

Right now, I'm focused on tightening a specific lemma that turns out to be of independent interest and is used in a few other contexts also.

For a given n x n matrix X with coefficients in C, let ||X|| denote the Frobenius norm. (The Frobenius norm is essentially just Euclidean distance where one treats each matrix coefficient as two Euclidean coordinates, one from its real part and one from its imaginary part.)

Lemma: Let A and B be unitary matrices, and let C be the commutator of A and B (that is, C=ABA^(-1)B^(-1)). Then || I - C ||^2 <= 2|| I -A ||^2... (read more)

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