• An excluded subobject theorem for nondistributive lattices

    I gave a talk yesterday at the PMC’s SASMS. I typeset some notes, and I thought I would share them because I drew pictures. This typeset version has more details and less visual intuition than what I presented on the blackboard, which is why the whole thing fit into a half hour. Find a link to the notes and some flavour text under the cut...

  • sl(2) for Combinatorialists

    There is a long and terrific story to tell about Lie theory, and I wish I could do it justice, but there’s far too much to say in a single post. What I have today is merely one application of one Lie algebraic idea, which ends up being a useful theoretical and practical tool in enumerative combinatorics...

  • Graph Homomorphisms and Cores

    Today I’d like to talk about an open problem I’ve been interested in for the past couple of years. It’s a very hard problem, in that there are easier special cases that are famously unapproachable, but it makes for some rather pretty algebra, living at the intersection of graph theory and category theory. If you ask me, it’s too good to be false...

  • A Few Translation Exercises

    One of my favourite books is Gödel, Escher, Bach, by Douglas Hofstadter. If you’re patient enough to read it all, I highly recommend it: it’s a great book about mathematics and cognitive science. ¶ One of the main goals of the book is to motivate, and sketch a proof of, Gödel’s first incompleteness theorem. At one point, he provides some exercises in transcribing number theoretical statements in a specific implementation of Peano arithmetic he calls TNT...

  • A Diophantine Contest Problem

    This is a shorter post, about a silly little problem I came up with a few months ago. It’s not a very intelligent problem, in that it doesn’t really serve any mathematical purpose; nor is it altogether tough; but I think it has a certain aesthetic pleasantness to it...

  • The call/cc Yin-Yang Puzzle

    The call/cc yin-yang puzzle is an ancient piece of Scheme code, which was written—or more accurately discovered—by David Madore in the year 1999 upon his invention of the esoteric programming language Unlambda. It is a rite of passage for aspiring Schemers to grok these five lines, if they claim true mastery over the power of the continuation...

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