Christopher Perez @_c_perez@mathstodon.xyz
University of Illinois at Chicago
Geometric Group Theorist
http://math.uic.edu/~perez
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."
New entry!
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...
URL: http://arxiv.org/abs/1707.03811v1
PDF: http://arxiv.org/pdf/1707.03811v1
Entry: http://read.somethingorotherwhatever.com/entry/Computationalcomplexityand3manifoldsandzombies
Like, doing this just feels weird: \( \bigcirc_{i=1}^nf_i := f_1 \circ f_2 \circ \dots \circ f_n \)
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.
http://briss.sourceforge.net/
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.
j2kun.github.io/math-genealogy/index.html
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.
University of Illinois at Chicago
Geometric Group Theorist
http://math.uic.edu/~perez
