Three days

What I learned over the last three days, mostly doing Softcover stuff:

  • Don’t put tex into markdown files and then convert it to tex. It is a disaster with so many \^{} and \textbar{} and ***(&@#($8 that you will hate yourself for a little while.
  • This occurs when you start with markdown in Softcover and then realize you can just use LaTeX, wonderful LaTeX, or more precisely the PolyTeX that Softcover uses.
  • This mistake of putting TeX or LaTeX in markdown files also causes a lot of errors because \[ \] is changed into \[ ], which is not display math anymore.
  • There is a lot of power in the Softcover setup. Power comes with pain. I set up some beautiful additions to the formatting of the pdf files, using the tcolorbox package to make pretty example formats. They look great in the pdf output. They don’t appear at all in the html, epub, or mobi output. Still worth it? Yeah…
  • Some things are still missing. Wish I could embed interactive graphics. Will think about it.
  • Oh. Netstat and sudo. I initially couldn’t even run the Softcover server on my computer. It uses port 4000, and running “softcover server” resulted in an error message saying that the port was in use (see previous post). The classic solution is to use ps aux | grep ruby or ps aux | grep rails to find your zombie ruby/rails processes — but I had none. The next most classic solution is to use netstat to find out what’s on that port: nothing but *.*. I tried lsof to listen. Nothing. WTF? I could start Rails on 3000, Sinatra on 4567, so it wasn’t a problem with either of those. Finally I thought to sudo netstat. Sudo! The magic handshake. Found “terabase” on there. What? NoMachine, something I long ago downloaded for VPN access to the U, was taking up port 4000 secretly. I haven’t used that in years — the math department/U switched to FastX a while back. Mystery solved — removed NoMachine and the Softcover server started like a charm without modifying the port. And I learned about netstat.

Anything else? Infinite matrices are weird. Nilpotent orbits seem useful. Givental is publishing a selection of tapas about quantum K-theory — quite interesting. Time for bed.

Where did I put those command-line tools?

What I learned last night:

  • Upgrading my operating system (on a Mac) lost me the command-line tools from XCode.
  • Yes, I remember this was a problem last time around but everything had been going so smoothly that I forgot.
  • Mysterious errors: why wasn’t Nokogiri working anymore? It totally worked last time. What’s this error message about libiconv? (Yep, I upgraded in New York so that I could use Matlab, and being on the road until last week I hadn’t touched anything that depended on Nokogiri.)
  • Well, Nokogiri actually has a really useful installation page! It explicitly addresses that libiconv error, reminding me of the command-line tools problem. Easily fixed.

I was going through this to update my Softcover installation, as I’m curious about using Softcover to create books that use LaTeX and publish nicely to HTML, epub, mobi, and pdf. For this kind of thing — books in chapters with subchapters, sections, figures, tables — you really do need some sort of structure on an almost mechanical level, and XML and HTML are such structures. But then how do you read parts from your book, putting it together and taking it apart in the appropriate ways? Nokogiri is a package of code that parses HTML, XML, and more. It’s pretty important to the way Softcover works.

One other problem with the Softcover install: putting epubcheck-3.0 in the right place. The installation instructions say “put it in your path!” but I found some difficulty as simply putting it in my path did not render it discoverable to the softcover check process. This discussion helped a bit — putting it in /bin/ worked nicely.

Now I just need to figure out why “softcover server” is not working…. all the hints I’ve seen to deal with “in `start_tcp_server’: no acceptor (port is in use or requires root privileges) (RuntimeError)” have failed to address the problem.

Back to the whirlpool

The semester is starting soon, but today I got sucked into the whirlpool of pure math. You read one thing and do some calculations and then you find another thing and then you follow a link to another and there you are: it’s 4 pm and you’ve found all kinds of things about multidegrees but you didn’t answer the original question.

So what did I learn? The following is clearly aimed mostly at myself, as I’m not exactly explaining anything for an audience here.

  • Multidegrees: they’re polynomials that sort of generalize the concept of “degree” in algebraic geometry, which in turn generalized the idea of “degree” that you might remember from algebra (x^2 + 3x is a degree two polynomial, because it intersects with a generic line in two places, more or less).
  • The current cool reference is Miller and Sturmfels’ Combinatorial Commutative Algebra, in chapter 8. Their approach is very algebraic, to me, and I got stuck on some of the simple examples right away and had to go refresh my memory on how they work with multigraded rings. I learned some things about Smith normal form that I don’t think I ever knew.
  • However, I really love Chriss and Ginzburg’s Representation Theory and Complex Geometry, and they discuss the same exact polynomials but they call them equivariant Hilbert polynomials. They make the point that it’s a generalization of the Hilbert polynomial. Cool. But I have to admit I still found parts of their exposition somewhat difficult as well.
  • In 2011 a guy named Gergely Berczi gave some Impanga lectures that covered these polynomials, too, and in his summary I found the most natural presentation of the polynomials. In the correct situation, looking at a T-invariant subset C of a G-representation V, the multidegree (polynomial) mdeg(C,V) is just the product of the equivariant weights in the normal direction. That, to me, is a very nice intuitive description, and explains why the multidegrees are double Schubert polynomials in some very special situations!
  • Some people call multidegrees “equivariant Poincare duals” and others call them “Joseph polynomials,” it looks like.

Fine. I guess I will turn to my administrative stuff now for a short time and then it is time for dinner and the rest of life!

Right: some of these links to Amazon are affiliate links so I might make some tiny amount of money if you buy one of these lovely math books via such a link. I don’t recommend any math books in this post I don’t have myself 😉

A stationary point

After Manhattan -> Jyväskylä -> Kilpisjärvi -> Oslo -> Toronto, I’m back in MN. That’s the ARPM bootcamp in New York and met lots of cool quant-y people, then Finland and uncles and aunts and just one sister :), then Lapland with the in-laws for an amazing few days of hiking, then Oslo to visit a cousin and enjoy Norwegian civilization. And then the Actuarial Research Conference, where I learned more about current trends in actuarial research than I ever knew. Truly.

Now I’m back to Minnesota, being bitten by mysterious insects in the garden. On the plus side, we’ve got corn and squash and herbs galore. On the minus side, not weeding for four weeks of rain and sun was the expected disaster.

  • Upgraded my Matlab skills a bit at ARPM bootcamp and need to work to extend them. Upgraded my knowledge of portfolio selection even more — this is going to change how I teach my intro to math for finance course at the U!
  • Learned a lot from Sarah Mathieson, Head of Research and Knowledge at the Institute and Faculty of Actuaries, about climate change, sustainability, and what actuaries are doing to understand how this will affect insurance and global markets. This is an interest of mine that I’ve been approaching from different angles for a while — clearly the linked EarthCalculus material doesn’t have finance involved yet, but take a look at previous posts for a peek at the weather derivatives research I’ve been doing.
  • Speaking of earth-y stuff, in Kilpisjärvi I saw voles and lemmings and a least weasel and all sorts of birds and lichen. I need to share those pics and some of those experiences! They were so cool, and arctic ecology is both changing as our climate changes and has tons of math….
  • Speaking of math and math ed, my friend Rob Edman wrote a post on the IMA Math Modeling Camp this summer. I worked on it last year and led two groups who looked into mercury toxicity in small and large-mouth bass in the Mississippi, but this year I was in Finland.
  • The semester will start soon. If I’m going to overhaul FM 5001/5002 and improve our online probability learning resources, there’s a lot to do! Recorded two probability problem-solving videos today; need to edit and post them tomorrow.

Ok. Did you know that undocumented immigrants generated surplus Medicare contributions of $35.1 billion between 2000 and 2011? That extended the solvency of Medicare for a year. Reference: Journal of General Internal Medicine, June 23, 2015. This is what you get to hear about when you have a health care policy wonk spouse. And now it’s time for bed.