True Logick is Neohermetic Pythagoreanism for the the modern mathematician.

I want to use the phrase “fire up the Rips machine” in my thesis.

How to threaten a mathematician: "This is some nice Hagoromo Fulltouch chalk you have here. It would be a shame if you came into your office one day and found it broken to pieces on the floor."

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Computational complexity and 3-manifolds and zombies
Article by Greg Kuperberg and Eric Samperton
In collections: Attention-grabbing titles, Basically computer science
We show the problem of counting homomorphisms from the fundamental group of a homology \(3\)-sphere \(M\) to a finite, non-abelian simple...
Entry: read.somethingorotherwhatever.

Like, doing this just feels weird: \( \bigcirc_{i=1}^nf_i := f_1 \circ f_2 \circ \dots \circ f_n \)

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Idle thought: with the exception of \( \sum \) and \( \prod \), transforming an associative binary operation into an agglomerative "summation notation" is just making the symbol big and adding sub/superscripts. E.g., \( \bigotimes_{i=0}^n v_i \). It's strange to me that this applies to non-commutative operators ( \( \wedge \) ), but also that there are many binary operations where this rule can't be applied due to limitations of the syntax (bracket operators, function composition, modulo).

I recently learned about Ologs, which are basically "category theory for normal people". These are very useful for knowledge representation. I am now in the making of a blog post about how to make them and how to translate ologs to Haskell code.

I recently found some hilariously-named software that cuts PDFs scanned as two pages side-by-side into single pages.

Let \(Y\) be a subspace of \(X\). The wizard hat space \(W\) is constructed by attaching the base of the cone \(CY\) over \(Y\) to \(X\) along \(Y\).

(This showed up in a topology class I took once. We needed to use the fact that \(W\) deformation retracts onto \(X\), but I don't remember what it was used for. The name is mine.)

Math genealogy visualizer now supports finding the closest common ancestor of two mathematicians.

Working on my thesis project. Given two torsion-free groups \(\Gamma_1,\Gamma_2\) which are elementarily equivalent and both hyperbolic relative to their abelian subgroups, I'm currently trying to determine what sorts of constraints I can put on how homomorphisms \(\Gamma_1\to\Gamma_2\) behave on the abelian subgroups.


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