Tag Archives: moduli space

Back from Boston

I spent the end of last week in Cambridge, where I gave a talk at MIT about the homology of Hurwitz spaces.

  • Good addition to Harvard Square: there’s now a used-book table on Mass Ave, like the ones I used to patronize on Broadway in Morningside Heights. I flipped through “Strike From Space,” a 1965 book by Phyllis Schlafly and Lester Ward, with the thesis that dopey Democrats were getting head-faked by the Soviets into escalating our commitment to Vietnam, which conflict was in fact not the firewall against an all-red Asia but a mere Soviet plot to distract us from an imminent nuclear first strike from orbit. Bad addition to Harvard Square: a Qdoba! I thought fast food was forbidden from Harvard Square by zoning laws, but apparently you can apply for an exemption — here’s Chipotle’s application to open a restaurant at One Brattle Square.
  • I had the pleasure of meeting Andy Putman and learning about a beautiful recent theorem of his; the moduli space of genus-g curves with full level N structure has the same second homology as M_g itself, for g at least 5. As a corollary, all these spaces have Picard number 1. I also learned a lot from Denis Auroux about mapping class group factorizations and symplectic Lefschetz fibrations — but more on this when I write a post or two on Hurwitz spaces.  Update: (25 Sep 08) Putman’s paper is now on the arXiv.
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The moduli space of senators and the moduli space of movies

Last week I blogged about Dmitri Tymoczko’s lecture and the moduli space of chords; since then I remembered some more nice examples of “moduli spaces” in the loose sense described in that post. One comes from the work of Keith Poole and Howard Rosenthal, who attempt to answer the question: what is the best way of “mapping” the members of a legislature in two-dimensional space so that two legislators are close together precisely when their voting records are very closely aligned? In other words, what is the moduli space of senators? Go to Poole’s VoteView page and scroll to the bottom to see the last 100 years of the House and Senate as an animated .gif. Or just read what I wrote about their research on Slate. (Article from 2001, so some links may be dead.)

Votes in the Senate make up a complicated dataset, which people like Poole and Rosenthal like to make more accessible by means of two-dimensional charts. An even more complicated dataset is the set of 100,000,000 Netflix ratings of 18,000 movies which the strivers for the Netflix Prize have to wrestle with. But this too can be nicely mapped into two-dimensional space (or any-dimensional space, but two-dimensional pictures are the easiest to look at!) yielding a “moduli space of movies” in which two movies are close together just when they tend to be liked by the same set of users. Todd Holloway, a CS grad student at Indiana,has made some beautiful examples:

Go to his blog to see the interactive version, or his visualization of the power struggle in Wikipedia.

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