Apr 5, 2013 You can now see the list of talks at Category-Theoretic Foundations of Mathematics Workshop at the Department of Logic and Philosophy of Science of U.C. Irvine, May 4-5, 2013. Elementary ...

Define the Standard Model gauge group to be S ( U ( 2) × U ( 3)), the subgroup of SU ( 5) consisting of block diagonal matrices with a 2 × 2 block and then a 3 × 3 block. (This is isomorphic to the ...

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 ...

Last summer my students Brendan Fong and Blake Pollard visited me at the Centre for Quantum Technologies, and we figured out how to understand open continuous-time Markov chains! I think this is a ...

I move jobs tomorrow: from Glasgow to Edinburgh, city of James Clerk Maxwell, Arthur Conan Doyle, Robert Louis Stevenson and Dolly the Sheep. But before I go, I want to give you the fourth and final ...

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 ...

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 — ...

Example: suppose we have a data structure representing an abstract address. An address is, alternatively, an email address or a postal address like in the previous example. We can try to extract a ...

Bless British trains. A two-hour delay with nothing to occupy me provided the perfect opportunity to figure out the relationships between some of the results that John, Tobias and I have come up with ...

It’s an underappreciated fact that the interior of every simplex Δ n \Delta^n is a real vector space in a natural way. For instance, here’s the 2-simplex with twelve of its 1-dimensional linear ...

Summer saw the foundations of mathematics rocked by the publication of The HoTT Book. Here we are a few months later and the same has happened to physics with the appearance on the ArXiv of Urs’s ...

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 ...