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 ...

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 ...

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 ...

Peter Scholze has just published a challenge to the automated mathematical formalisation community in a post – Liquid tensor experiment – on Kevin Buzzard’s blog. Peter explains there the motivation ...

Hello (none)@40.77.167.4.So nice of you to stop by. I'm a member of the Theory Group here at UT. I've been at UT since September 1994. Before coming here, I was an Assistant Professor in the theory ...

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 ...

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 ...

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 ...