The Romans (among others!) wrote in wax with a stylus; the wax was embedded in boards, which were bound together in pairs. If a Roman were to place clay between these boards, could they make a copy of their wax tablet in the clay?

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I gave a talk in the Farb and Friends Student Seminar (back in March!) on:

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I'll briefly introduce the Lights Out puzzle: the game is played on an n-by-n grid of buttons which, when pressed, toggle between a lit and unlit state. The twist is that toggling a light also toggles the state of its neighbors (above, below, right, left—although, on the boundary, lights have fewer neighbors). All the buttons are lit when the game begins, and the goal is to turn all the lights off.

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I made a movie recently for my advisor. The movie is so pretty, that I thought I'd share it here: may I present to you randomly drawn dots, where two dots are the same color when they touch!

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In this fun paper,

MR1845679
it is pointed out that
  • homology is a very basic invariant, and
  • closed manifolds are very basic objects
and so a very basic question is: what sequences of abelian groups are the homology groups of a closed simply connected manifold?

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I'm again applying Granger causality to time series data from Intrade. This time, however, I connect box A to box B with a

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Granger causality is a technique for determining whether one time series can be used to forecast another; since the Intrade market provides time series data for political questions, we can look at whether political outcomes can be used to forecast other political outcomes.

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I made some movies of some of my favorite complexes: let $I^n$ be the $n$-dimensional cube, and let $e_1, \ldots, e_n$ be the $n$ edges around the origin, and let $e_i e_j$ be the square face containing the edges $e_i$ and $e_j$. Define a subcomplex $\Sigma^2_n \subset I^n$ consisting of the squares $$e_1 e_2, e_2 e3, \ldots, e{n-1} e_n, e_n e_1$$ and all the squares in $I^n$ parallel to these. It turns out that $\Sigma^2_n$ is a surface with a lot of symmetries.

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Drew Hevle raises a very interesting question: suppose you are stranded on a desert island; what books would be entirely useless in this situation?

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The pineapple sauce pancake graph has English words as vertices, and a directed edge from $a$ to $b$ if the concatenation $ab$ is also an English word. For instance, there is a vertex labeled pine, and a vertex labeled apple, and an edge from pine to apple.

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