In this post I want to describe the following result, which I think is pretty neat and should be more widely known:
Theorem: On the category of (small) categories there is a unique model structure in which the weak equivalences are the equivalences of categories.
In February there is going to be a workshop and school dedicated to exploring the interactions of Quantum Gravity, Higher Gauge Theory, and Topological Field Theory. I’m excited about the chance to share ideas and hopefully create some new mathematics.
The conference will take place in Lisbon, Portugal, and yours truly will be giving one of the mini-courses for the school (the topic is going to be the classification of extended 2D tqfts, something near and dear to my heart). Of course that makes me really excited, but I am also excited about the other topics too and I think the mix of ideas will be invigorating. For more info look below the break.
Today is the Birthday of MathOverflow. So go celebrate by asking or answering a question!
I am currently taking course notes for Jacob Lurie’s class on Chromatic Stable Homotopy in real time in Latex. This is not the first time I have taken course notes live and in tex, and when people see it happening they often ask me about it.
I wanted to write an update about Jacob Lurie’s class on Chromatic Stable Homotopy and mention some of exciting and beautiful things happening in that course, but as I started writing this post I found that it was morphing into a sort advice post on how to LaTeX in real time. Since there is obvious appeal, I’ve decided to run with it and collect all the advice, tips, and tricks on how to LaTeX in real time that I’ve gathered from the wild.
Now that we’ve all gotten over the excitement surrounding the new iPad, I wanted to talk about something else which I actually find very exciting (unlike the iPad). This semester Jacob Lurie is giving a course on Chromatic Homotopy Theory. This is a beautiful picture which relates algebraic topology and algebraic geometry. Hopefully with Jacob at the helm we’ll also see the derived/higher categorical perspective creeping in. This seems like a great opportunity the learn this material “in my heart”, as my old undergraduate advisor used to say.
And with most of our principal bloggers distracted by MathOverflow, it also seems like a good time to experiment with new media. So here’s the plan so far:
During lectures I’m going to be live-TeXing notes, which I’ll flush out and post to my website. (Jacob’s also posting his own notes!)
In addition, I’ll try to post blog articles (like this one) about related topics or topics I find interesting/confusing.
There might be a little MO action thrown in for fun.
The offshoot is that today I want to talk a little about chromatic homotopy and about the Atiyah-Hirzebruch Spectral Sequence.
So I’ve recently been thinking a lot about lax functors between n-categories, trying to get a better feel for what they are and why we should care. I have a few ideas about how certain lax functors could eventually be useful for TQFTs, but ever since I asked this question on MathOverflow I have started to doubt that lax functors in themselves are really good for anything.
So I’ve finally managed to bang my dissertation into something more or less ready for public consumption. It is basically finished (except for some typos and spell checking).
It is available on my new website.
The title is “The Classification of Two-Dimensional Extended Topological Field Theories”.
There has been some recent discussion about tikz and beamer and I wanted to throw my two cents into the mix. What better way then by showing off the slides I used last week to talk about my dissertation? I had a lot of pictures, all of which I made entirely in tikz. Here is the link.
This morning Jacob Lurie posted a draft of an expository paper on his work (with Mike Hopkins) classifying extended (infinity, n)-categorical topological field theories and their relation to the Baez-Dolan cobordism hypothesis.
Should make for some intersting bedtime reading…
This link was posted on the topology list a while ago and I thought it was too cute not to pass along.
My favorite is Boy’s surface!