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.Read More →
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.
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:
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.
Some links which I made during the talks:
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.Read More →
Some notes to myself on working with DJVU and PDF.
To convert a DJVU file to PDF:
ddjvu.eve -format=pdf -page=1-10 infile.djvu outfile.pdf
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?Read More →
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.