# Blog of Matthew Daws

## Stalled work

Cleaning out my desk, I came across some plans for further work on predictive policing. It now seems rather unlikely I will have time to pursue these (what with a fixed number of hours in a day, and a desire to be a research in Mathematics, at least at the moment). I thought I might as well record the ideas here.

## Notes

A couple of new research notes:

• Some notes on inductive limits of Banach spaces and algebras. I don't have a use for this rather esoteric topic, but a couple of textbooks make (slightly) wrong claims, so I wrote up some notes and carefully checked how far we could get things to work.

• A quick proof showing how to get the Kaplansky Density Theorem by using Arens products, and "elementary" (for various values of elementary) $$C^*$$-algebra theory.

## Maps

Because of lockdown, and the desire to occasionally get out the house, I have been exploring the local area more closely. The following are some nice resources:

## TALMO

I've spent yesterday afternoon and this morning attending the TALMO conference, from the comfort of my home office, via Zoom. The extremely efficient organisers have already got many of the presentations uploaded to YouTube.

• OBS Virtualcam : OBS is a great (free) screen recorder which allows e.g. composing different inputs (so overlaying a webcam image at an arbitrary place in a screen capture of just one window). The "Virtualcam" is an output which fakes up a new webcam on your system, hence allowing you to pipe the OBS output into any application which uses a webcam.
• Accessibility talk slides : This has been rumbling away in the background, but an unhappy confluence of a looming deadline just as we add more things online makes it more important. Particularly discussed was Bookdown. Perhaps it is time to move all my lecture notes to a new format. But it's the input of time required, and a new toolchain to learn...
• Xournal++ (a fork of Xournal into C++ I think leads to the title) is a FOSS PDF annotator that supports LaTeX. Next time I am marking work I will investigate this.
• There was a question asking about Tablets. Suggestions included Wacom tablets, and those by xp-pen
• Videos to help students adapt from A-Levels which is especially important this year, as most students will have missed the end of their A-Level studies. There was some talk that the AMSP would be doing something, but I couldn't find much (at a brief glance).

## Genetics and ancestry

What feels like a lifetime ago (before some other genetics happened) I listened to Adam Rutherford's book of the week "How to Argue With a Racist" on Radio 4. It's now been so long that the Radio 4 link is dead, but you can buy the book or read the book review. The radio series was interesting, but one particular (slightly off topic) point I remember. Adam claimed (I mean, I think, it was a while ago) something like

Go back around 11 generations, and you will have ancestors who share none of your genetic material.

What argument might lead to this conclusion? My main initial conclusion was that I did not really know how inheritance works at the genetic level.

## DJVU and PDF

Some notes to myself on working with DJVU and PDF.

To convert a DJVU file to PDF:

• Use ddjvu.eve -format=pdf -page=1-10 infile.djvu outfile.pdf
• Manual: http://djvu.sourceforge.net/doc/man/ddjvu.html Notice in particular docs about quality, using JPEG compression etc.
• Source: https://superuser.com/a/571787/503838

## New preprint

Well, not new really, just I forgot to blog about it. "Ring-theoretic (in)finiteness in reduced products of Banach algebras" with Bence Horváth (currently a postdoc at the Czech academy of sciences). Available at arXiv:1912.07108 [math.FA]

We look at ultrapowers and the asymptotic sequence algebra of Banach algebras. There has been some interest recently in using tools from Model Theory (specifically, the recent area of "Continuous model theory") to study such objects for $$C^*$$ and von Neumann algebras. One of our research themes is that things do not work so nicely for Banach algebras, and in particular, one often has to get one's hands dirty (and not use Model Theory results) because Banach algebras are not very "metrical" objects, unlike operator algebras. We construct various counter-examples, and also leave open some tantalizing questions about renormings of some rather concrete algebras.

I worked (in a very "bare hands" way) on ultraproducts in my thesis, and shortly afterwards, and it was fun to return to this topic, but to take a slightly more abstract approach. Something we wrote in the introduction is that we wonder if the asymptotic sequence algebra of a Banach algebra could be an interesting source of (counter-)examples for other problems?

## Graduate Course 2020 part 2

The 2nd part of my talk to postgraduate students is all about statistics, particularly hypothesis testing, and why I like Bayesian approaches. As the room allocated was long and thin with whiteboards only on the long walls, I decided that a chalk-and-talk would just lead to neck ache in my audience.

So I want with a beamer talk (pdf of slides) which inevitably lead to me finishing early. I guess no-one minded this.

A mini-bibliography:

• I still really enjoy my undergraduate lecture notes curtesy of Prof. Richard Weber (I feel old to see that Prof Weber is now retired...)
• Rice, "Mathematical Statistics And Data Analysis" which said lecture notes follow moderately closely. Amazon link. Also available in the UCLAN library.
• A wonderful book is MacKay, Information Theory, Inference, and Learning Algorithms. Available in electronic format for free.
• A more straight-up introduction to Bayesian thought is Sivia and Skilling, "Data Analysis: A Bayesian Tutorial". Amazon link. This book blends some philosophical thoughts (but not overly heavy) with practical and interesting advanced statistics. I believe it's available online from one of the online libraries UCLAN subscribes to (and/or is in the library).
• A more heavy-weight alternative is Bayesian Data Analysis, Third Edition by the gang of six. Amazon link.
• A bed-time book is the excellent Nate Silver's book "The signal and the noise". Amazon link. Everyone should read this.