Apr 7, 2009 Here are the slides for a talk explaining some hypotheses relating n-categories and topology, and Jacob Lurie’s new work on these hypotheses. Ben-Zvi’s Lectures on Topological Field Theory ...

The discussion on Tom’s recent post about ETCS, and the subsequent followup blog post of Francois, have convinced me that it’s time to write a new introductory blog post about type theory. So if ...

The following is the greatest math talk I’ve ever watched! Etienne Ghys (with pictures and videos by Jos Leys), Knots and Dynamics, ICM Madrid 2006. [See below the fold for some links.] I wasn’t ...

Freeman Dyson is a famous physicist who has also dabbled in number theory quite productively. If some random dude said the Riemann Hypothesis was connected to quasicrystals, I’d probably dismiss him ...

I don’t really think mathematics is boring. I hope you don’t either. But I can’t count the number of times I’ve launched into reading a math paper, dewy-eyed and eager to learn, only to have my ...

But for some reason I’ve never studied crossed homomorphisms, so I don’t see how they’re connected to topology… or anything else. Well, that’s not completely true. Gille and Szamuely introduce them ...

Most recently, the Applied Category Theory Seminar took a step into linguistics by discussing the 2010 paper Mathematical Foundations for a Compositional Distributional Model of Meaning, by Bob Coecke ...

In order to get used to the calculus of exact squares, the first thing we have to change is to start thinking more in terms of Kan extensions rather than limits and colimits. For instance, it’s usual ...

Whether we grow up to become category theorists or applied mathematicians, one thing that I suspect unites us all is that we were once enchanted by prime numbers. It comes as no surprise then that a ...

I want to talk about some attempts to connect the Standard Model of particle physics to the octonions. I should start out by saying I don’t have any big agenda here. It’d be great if the octonions — ...

When is it appropriate to completely reinvent the wheel? To an outsider, that seems to happen a lot in category theory, and probability theory isn’t spared from this treatment. We’ve had a useful ...

Over the last few years, I’ve been very slowly working up a short expository paper — requiring no knowledge of categories — on set theory done categorically. It’s now progressed to the stage where I’d ...