Why Mathematics is Boring. 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 ...

Here’s my second set of lecture notes for a 4 1 2 \frac{1}{2}-hour minicourse at the Summer School on Algebra at the Zografou campus of the National Technical University of Athens. Part 1 is here, and ...

These are some lecture notes for a 4 1 2 \frac{1}{2}-hour minicourse I’m teaching at the Summer School on Algebra at the Zografou campus of the National Technical University of Athens. To save time, I ...

The monoid of n × n n \times n matrices has an obvious n n-dimensional representation, and you can get all its representations from this one by operations that you can apply to any representation. So ...

Current itex2MML Version: 1.6.1 (10/3/2021) Installation: Readme Source code: (download | browse repository) Here is a list of all the TeX commands currently implemented in itex2MML. Most should be ...

I was really happy to understand this construction, both the fact that ℂ \mathbb{C} on categories (and in particular, on Δ \Delta) coincides with the comonad resolution, and the resulting description ...

Just to add to Todd’s beautiful comment about bar-construction. There is another interpretaton of bar-construction as a resolution. The following construction is in my paper “Categorical Strong Shape ...

By the way, my proof here that the ring of symmetric functions Λ \Lambda is the free λ \lambda-ring on one generator is a bit ‘tricky’, since I was wanting to deploy things we’d already shown and not ...

A mathematician hands out a pack of cards to a group of five people. They repeatedly cut the deck and then take a card each. The mathematician tries to use telepathy to divine the cards that the ...

For questions 1 and 2, isn’t that true for any group G, not just the fundamental groups of a manifold? And moreover, I think of this as the definition of the profinite completion of a group: as an ...

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 you’ve ...

The same day as the “Lessons from the LQG string” appeared on hep-th, there was another paper by Corichi, Vukasniac and Zapata crosslisted from gr-qc discussing the loopy oscillator and coming to ...