## Lamb and black truffle sausage: Osteria Papavero, you crazy bastard, I love you

One of the appetizers at Osteria Papavero is “antipasti di tartufo” — three dishes with black truffle, subject to chef’s whim and different every night.  Truffle is one of those ingredients that I know is distinguished and I know is expensive but which has never really revealed its charms to me.  Papavero is helping me out with that problem.   I think I’m going to go ahead and order this dish every time I go, because it’s consistently the highlight of the meal.

Tuesday night, one of the plates was a truffled lamb sausage. Long, dark brown, a little pocked, served in a loose coil, looking a little disturbingly like — well, I’ll bet you can guess what it looked a little disturbingly like.  But it was superb:  coarsely ground, a little gamy or smoky, and rich as hell, without being, you know, stupidly rich.  One of the best things I’ve eaten in Madison.

Papavero has a Christmas tree with comic photos of the staff in place of ornaments.  Also a Xerox of the greatest New Yorker cartoon of all time:

Image courtesy of a post by Daniel Radosh, who observes that the caption is not identical with the one that originally ran in the magazine.  But this version is the one I know and admire.

## In which I improve on Sting

The worst lyric Sting ever wrote, obviously, was

It’s no use, he sees her, he starts to shake and cough

Just like the old man in that book by Nabokov

But if he’d changed the last line to

Just like the robot in that book by Asimov

it would have been the best lyric he ever wrote.

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## The best math joke that will appear in a major Hollywood picture this year

Early in the just-released Up in the Air, George Clooney’s character reveals to a young coworker his dream of registering 10 million frequent flyer miles on American Airlines.  She responds dismissively, “Isn’t 10 million just a number?”

Clooney replies — with just the right weary exasperation — “Pi is just a number.”

It’s a good movie, by the way, better than I expected from the trailer.  It doesn’t try to do anything very hard and it possesses simple virtues:  good writing, good acting, good pacing.  Then again, almost every movie I see lacks at least one of these; so in this sense Up in the Air tried something hard after all.

By the way, I can no longer hear Clooney’s name without thinking of the recorded “Doors Closing” announcement on the DC Metro.  It really does sound exactly like a voice warning you, softly, robotically, and somehow wistfully, “George Clooney.”

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## Square pegs, square pegs. Square, square pegs.

Lately I’ve been thinking again about the “square pegs” problem:  proving that any simple closed plane curve has an inscribed square.  (I’ve blogged about this before: here, here, here, here, here.)  This post is just to collect some recent links that are relevant to the problem, some of which contain new results.

Jason Cantarella has a page on the problem with lots of nice pictures of inscribed squares, like the one at the bottom of this post.

Igor Pak wrote a preprint giving two elegant proofs that every simple closed piecewise-linear curve in the plane has an inscribed square.  What’s more, Igor tells me about a nice generalized conjecture:  if Q is a quadrilateral with a circumscribed circle, then every smooth simple closed plane curve has an inscribed quadrilateral similar to Q.  Apparently this is not always true for piecewise-linear curves!

I had a nice generalization of this problem in mind, which has the advantage of being invariant under the whole group of affine-linear transformations and not just the affine-orthogonal ones:  show that every simple closed plane curve has an inscribed hexagon which is an affine-linear transform of a regular hexagon.  This is carried out for smooth curves in a November 2008 preprint of Vrecica and Zivaljevic.  What’s more, the conjecture apparently dates back to 1972 and is due to Branko Grunbaum.  I wonder whether Pak’s methods supply a nice proof in the piecewise linear case.

The alphabetical gourmands of Eating in Madison A to Z are up to  “Pizza ____.”  I recently tagged along on their visit to Pizza Oven on the West Side:  the resulting review just went up on their blog.  Seems a good time to set down some of my own thoughts on Madison pizza.

Ian’s:  Pizza without boundaries.  The experiments are exciting even when they don’t work.   I’ve blogged enough already about this cultural treasure. Today Milwaukee, tomorrow the world.  Glass Nickel is a worthy contender in the same genre — the Thai Pie, in particular, is an experiment that’s become a perfected piece of pizza technology.  Also, they have delivery trucks that run on pizza grease.

Thin crust pies.  The best is Pizza Brutta, on upper Monroe, which makes a very thin, irregular, faintly sweet crust with nice blackened bubbles around the rim.  The traditionalist to Ian’s mad scientist.  My second favorite place to eat pizza in Madison.  Try the Portabella.  Greenbush Bar and Cafe Porta Alba (just re-opened in Hilldale) have devoted followings, and are always packed, and make a good thin crust pie; but nothing to match Brutta.  Pizza Oven isn’t in the league of Greenbush and Porta Alba,  but is charming if you grew up in the suburbs in the ’70s, and you won’t need to wait for a table in this cavernous shed-like former Hooters.

Thick crust pies. I’m against thick crust pies.  I don’t even know who, if anyone, makes them here.

New York pies. The best is Casa Bianca, way out west on Junction Road.  I’m told on good authority that the proprietors are not actually New York Italians, but Macedonians who ran a pizzeria at home and kept it up when they moved to Wisconsin; and moreover that they train just-arrived Macedonian immigrants to make New York pies, then send them out to open New York pizzerias in other Midwestern cities that lack one.  Looking this up on Yelp, I see that Casa Bianca seems to have gone out of business.  But I’m leaving this up because I found the story about the Macedonian pizza entrepreneurship lab kind of heartwarming.  I guess your only choice for New York pie now is Pizza di Roma on State, which mimics the experience of getting a big floppy extra greasy slice at a no-name pizza counter in Manhattan pretty much exactly, for better or worse.

I haven’t tried and have no opinion about:  Rocky Rococo’s, Gino’s.  I’ve had mediocre Italian food at and thus have low expectations for the pizza at:  Porta Bella, Paisan’s.  I’ve had good Italian food at and thus have high expectations for the pizza at:  Osteria Papavero (lunch only) and Cafe la Bellitalia.   I am put off by the name of and thus have low expectations for the pizza at:  Pizza Extreme.

## Menopause Matters

It’s a little outside the usual stomping grounds of this blog, but I thought I’d mention that my cousin-in-law the doctor, Julia Edelman, has a new book out, Menopause Matters. Julia is the mom of this cousin-in-law, by the way.

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## RIP Miles “Teddywedger” Allen

Miles Allen, founder and proprietor of Myles Teddywedger at the top of State Street, died Friday of cancer.  No word yet on whether the Cornish pasty emporium will keep operating.  If not, it’s a real loss — no one else on Capitol Square really rivaled MT for a cheap, satisfying, almost instant meal.

## Evan Baden: The Illuminati, at Wisconsin Union

Five prints from Evan Baden‘s photo series The Illuminati are hanging now through January 19 in the 2nd floor galleries at the Wisconsin Union.  The idea is pretty simple:  photos of young people by the light of their computing devices.  But they’re beautiful.  Whoever curates photography at the Union is doing a very good job.

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## The Year in Mathematical Ideas

I have a short piece about Tim Gowers’ Polymath project in the 2009 edition of the New York Times Year in Ideas feature.

In January, Timothy Gowers, a professor of mathematics at Cambridge and a holder of the Fields Medal, math’s highest honor, decided to see if the comment section of his blog could prove a theorem he could not.

It’s been years since we’ve been New York Times subscribers; looking at Sunday’s paper I was struck by how much math was in it. In the Year in Ideas section, besides my piece, there’s one about using random walks to identify species critical to the survival of an ecosystem, another about the differential equations governing zombie diffusion, and a third about Nate Silver’s detective work on the fishy final digits of poll results.  (I blogged about DigitGate a few months back.)  Elsewhere in the paper, John Allen Paulos writes about the expected value of early breast cancer screening, and the Book Review takes on Perfect Rigor, Masha Gessen’s new biography of Perelman.  Personally, I think Gessen missed a huge commercial opportunity by not titling the book He’s Just Not That Into Yau.

## Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields

Now I’ll say a little bit about the actual problem treated by the new paper with Venkatesh and Westerland.  It’s very satisfying to have an actual theorem of this kind:  for years now we’ve been going around saying “it seems like asymptotic conjectures in analytic number theory should have a geometric reflection as theorems about stable cohomology of moduli spaces,” but for quite a while it was unclear we’d ever be able to prove something on the geometric side.

The new paper starts with the question: what do ideal class groups of number fields tend to look like?

That’s a bit vague, so let’s pin it down:  if you write down the ideal class group of the quadratic imaginary number fields $\mathbf{Q}(\sqrt{-d})$, as d ranges over squarefree integers in [0..X],  you get a list of about $\zeta(2)^{-1} X$ finite abelian groups.

The ideal class group is the one of the most basic objects of algebraic number theory; but we don’t know much about this list of groups!  Their orders are more or less under control, thanks to the analytic class number formula.  But their structure is really mysterious.