Author Archives: JSE

Idle question: are Kakeya sets winning?

Jayadev Athreya was here last week and reminded me about this notion of “winning sets,” which I learned about from Howie Masur — originally, one of the many contributions of Wolfgang Schmidt.

Here’s a paper by Curt McMullen introducing a somewhat stronger notion, “absolute winning.”

Anyway:  a winning set (or an absolute winning set) in R^n is “big” in some sense.  In particular, it has to have full Hausdorff dimension, but it doesn’t have to have positive measure.

Kakeya sets (subsets of R^n containing a unit line segment in every direction) can have measure zero, by the Besicovitch construction, and are conjectured (when n=2, known) to have Hausdorff dimension n.  So should we expect these sets to be winning?  Are Besicovitch sets winning?

I have no reason to need to know.  I just think these refined classifications of sets which are measure 0 yet still “large” are very interesting.  And for all I know, maybe there are sets where the easiest way to prove they have full Hausdorff dimension is to prove they’re winning!



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Erotische Flugblaetter

I was working in Memorial Library yesterday. Whenever I’m over there, I like to pull a book off the shelf and look at it.  (E.G.) I feel I have some kind of duty to the books — there are so many which will never be taken off the shelf again!

Anyway, there has never been an easier choice than Flugblatt-Propaganda Im 2.Weltkrieg:  Erotische Flugblätter.  How was I not supposed to look at that!  And I was richly rewarded.  The Nazi propagandists knew their business; the leaflets are written in perfect colloquial English, assuring American troops that the US government is purposely prolonging the war to keep unemployment low at home, that their kids and wives are pleading for them to come home alive by any means necessary (especially:  surrendering and riding out the rest of the war in a comfy German POW camp, with movies, sports, and the same food the German soldiers get) and, most of all, that their girlfriends back home, tired of waiting, are taking up with draft-dodgers and war-profiteers (especially the ruthless “Sam Levy.”)  UK troops got their own version:  their girlfriends weren’t making time with shifty Jews, but with US soldiers, who were “training” in England while the British men died at the front.

Some highlights:

photo 3 photo 2 photo 1

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Rachel Kushner (w/ comma poll)

From Rachel Kushner, The Flamethrowers:

I realized I’d been wrong.  She was not the pedigreed rich.  He was and she was not.  Sometimes all the information is there in the first five minutes, laid out for inspection. Then it goes away, gets suppressed as a matter of pragmatism. It’s too much to know a lot about strangers. But some don’t end up strangers. They end up closer, and you had your five minutes to see what they were really like and you missed it.

This is great!  My one question is about the commas in the last sentence.  If it had been me I probably would have omitted the comma after “closer,” but I sort of think Kushner’s version is better.  Then I wonder:  what about leaving the one after “closer” and adding another after “like”?

Hey, this is a good opportunity for a poll!  I’ve never put one in here before, let’s give this new WordPress functionality a swing.  (Non-standard comma used there on purpose, pedants.)

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Are UW-Madison professors underpaid?

It’s well known that UW-Madison salaries are notably lower than those at peer institutions, at every level of seniority.  But wait, says Chris Rickert in the Wisconsin State Journal, that doesn’t necessarily mean our faculty is underpaid!

At UW-Madison, assistants are paid, on average, about $82,000 a year, associates about $93,000 and full professors about $123,000 — ranking them 10th, seventh and 12th, respectively, in salary compared to 11 other state-identified peer institutions, according to data from the university’s Academic Planning and Institutional Research office.

Obviously, more full professors means more people in line for full-professor salaries and greater pressure on the budget for professorial salaries overall. At UW-Madison, that’s no small detail, as about 59 percent of UW-Madison professors have attained full status, according to the university’s Data Digest.

By contrast, figures from the American Association of University Professors show that, on average, only about 31.5 percent profs at all universities and about 30.8 percent at public universities are full professors.

This is a really good point!  You could imagine that maybe our pay isn’t underscale at all — maybe we just promote people faster, so that our full professors are less senior and thus make less.  That’s Rickert’s take:

I’m left to wonder whether the university has adopted that old human resources trick of placating employees by inflating their titles more than their pay.

In an era of declining state support, this would help keep a lid on the cost of higher education while simultaneously allowing university officials to complain about how poorly paid are its best and brightest.

But this can actually be checked!  You can use the Chronicle of Higher Education Faculty Salary Survey to get the mean salary for any university at any seniority level, and the number of faculty members at each seniority level, and compute the overall faculty mean that way.  I did this for a few of our peer institutions and got:

full $145 816 $123 755 $135 494 $139 943
assoc $96 556 $93 252 $90 407 $94 763
asst $90 405 $82 363 $77 329 $85 502
$117,133 $106,618 $104,595 $111,172

So the mean UW tenure-track gets paid slightly more than people at Iowa, but notably less than counterparts at Ohio State and Illinois.


Shin-Strenner: Pseudo-Anosov mapping classes not arising from Penner’s construction

Balazs Strenner, a Ph.D. student of Richard Kent graduating this year, gave a beautiful talk yesterday in our geometry/topology seminar about his recent paper with Hyunshik Shin.  (He’s at the Institute next year but if you’re looking for a postdoc after that…!)

A long time ago, Robert Penner showed how to produce a whole semigroup M in the mapping class group with the property that all but a specified finite list of elements of M were pseudo-Anosov.  So that’s a good cheap way to generate lots of certified pseudo-Anosovs in the mapping class group.  But of course one asks:  do you get all pA’s as part of some Penner semigroup?  This can’t quite be true, because it turns out that the Penner elements can’t permute singularities of the invariant folation, while arbitrary pA’s can.  But there are only finitely many singularities, so some power of a given pA clearly fixes the singularities.

So does every pA have a power that arises from Penner’s construction?  This is what’s known as Penner’s conjecture.  Or was, because Balazs and Hyunshik have shown that it is falsitty false false false.

When I heard the statement I assumed this was going to be some kind of nonconstructive counting argument — but no, they actually give a way of proving explicitly that a given pA is not in a Penner semigroup.  Here’s how.  Penner’s semigroup M is generated by Dehn twists Q_1, … Q_m, which all happen to preserve a common traintrack, so that there’s actually a representation

\rho: M \rightarrow GL_n(\mathbf{R})

such that the dilatation of g is the Perron-Frobenius eigenvalue \lambda of \rho(g).

Now here’s the key observation; there is a quadratic form F on R^n such that F(Q_i x) >= F(x) for all x, with equality only when x is a fixed point of Q_i.  In particular, this shows that if g is an element of M not of the form Q_i^a, and x is an arbitrary vector, then the sequence

x, g x, g^2 x, \ldots

can’t have a subsequence converging to x, since

F(x), F(gx), F(g^2 x), \ldots

is monotone increasing and thus can’t have a subsequence converging to F(x).

This implies in particular:

g cannot have any eigenvalues on the unit circle.

But now we win!  Because \rho(g) is an integral matrix, so all the Galois conjugates of \lambda must be among its eigenvalues.  In other words, \lambda is an algebraic number none of whose Galois conjugates lie on the unit circle.  But there are lots of pseudo-Anosovs whose dilatations \lambda do have Galois conjugates on the unit circle.  In fact, experiments by Dunfield and Tiozzo seem to show that in a random walk on the braid group, the vast majority of pAs have this property!  And these pAs, which Shin and Strenner call coronal, cannot appear in any Penner semigroup.


Anyway, I found the underlying real linear algebra question very appealing.  Two idle questions:

  • If M is a submonoid of GL_n(R) we may say a continuous real-valued function F on R^n is M-monotone if F(mx) >= F(x) for all m in M, x in R^n.  The existence of a monotone function for the Penner monoid is the key to Strenner and Shin’s theorem.  But I have little feeling for how it works in general.  Given a finite set of matrices, what are explicit conditions that guarantee the existence of an M-monotone function?  Nonexistence?  (I have a feeling it is roughly equivalent to M containing no element with an eigenvalue on the unit circle, but I’m not sure, and anyway, this is not a checkable condition on the generating matrices…)
  • What can we say about the eigenvalues of matrices appearing in the Penner subgroup?  Balazs says he’ll show in a later paper that they can actually get arbitrarily close to the unit circle, which is actually not what I had expected.  He asks:  are those eigenvalues actually dense in the complex plane?
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Ordinary business expense

From today’s NYT:

But even if Hyundai is eventually forced to pay the full amount of the damages, the punishment could be substantially reduced through a tax loophole that permits the company to save millions of dollars by deducting any court-ordered punitive damages as an ordinary business expense. The result, critics say, is that taxpayers are in effect subsidizing corporate misconduct.

What’s terrible about this isn’t that companies are allowed to claim the fines they pay for malfeasance are an ordinary business expense.  What’s terrible is that it’s true.

Update:  I misspoke, as a commenter points out.  A “fine” — that is, a penalty you pay to the government — is not deductible.  What may be deductible are punitive damages, paid to people you injured or whose river you despoiled.  Prepare your return accordingly!

Bad lesson

From the New York Times, “Why You Should Tell Your Children How Much You Make”:

When Scott Parker wanted his six offspring to know more about the value of money, he decided to do something that many parents would consider radical: show them exactly what he earned.

One day, he stopped by his local Wells Fargo branch in Encinitas, Calif., and asked to withdraw his entire monthly salary in cash. In singles. It took 24 hours for the tellers to round up that many bills, so he returned the next day and took away the $100 stacks in a canvas bag.

His oldest son, Daniel, who was 15 at the time, remembers the moment his father walked into the house and dumped the $10,000 or so on a table. “It looked like he had robbed a bank,” he said.

Parker was trying to teach his kids a lesson about the value of money.  But the lesson I would learn from this is “If somebody, like a bank teller, works in a service job, and makes a lot less money than I do, I can make them spend a full day of their life carrying out an incredibly tedious task without thinking about whether this is a reasonable way for them to spend their time.”





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Full professors make more money than bus drivers

Former Republican Congressional candidate and current UW-Madison history professor John Sharpless stands up for us against the Governor:

He said he arrives no later than 9 a.m. and leaves no earlier than 5 p.m. During that time, he said he’s either teaching, preparing lectures, doing research, attending required committee meetings, advising students and managing teaching assistants. Sharpless added that he often spends his evenings reading and grading papers.

“None of this seems like work to a guy like Walker because he lives a different life,” he said. “And I’m not going to make fun of what he does. I’m sure being a governor is a lot of work. He has to spend a lot of time in Iowa and South Carolina and North Carolina and courting other Republican big-wigs. That taxes the man horribly.”

But just to make it clear he’s still on board with GOP, he drops this in:

“I will retire with a salary that’s less than a Madison bus driver,” he said.

UW-Madison salaries are public records, so I can tell you that Sharpless’s is just under $80,000.  In 2012, only 9 employees of Metro made more than $70K.  And the ones who made that much, I’m pretty sure, are the ones who worked tons of overtime.

In other words, what Sharpless said is likely true in the strict sense of

“There exists a Madison bus driver whose salary this year exceeds mine”

but gives the wrong impression about typical full professors in the history department and typical bus drivers.

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Death to the 529 / long live the 529

Obama flip-flops faster than I can blog!  Prezzo has already walked back his proposal to change the 529 college-saving tax break, but I have a post about it queued up, and by gum I’m gonna publish it.

Here’s the plan that just got shelved.  From now on, capital gains on contributions you stow in a 529 plan won’t be tax free anymore — they’ll just be tax-deferred, as with a retirement plan.  In essence, it takes away a tax break whose benefit flows predominantly to high-income families (some 529 money is held by middle-income parents, but under Obama’s plan the $500 or so they’d lose on their 529 was more than offset by an AOTC expansion.)

OK, this Congress is as likely to roll back a tax break for high earners as they are to rename Reagan National Airport after Pete Seeger, so this isn’t actually happening, but I’m just saying, that’s the plan.

People are mad, and feel like they’ve been bait-and-switched. My FB feed, populated by dutiful savers like me, is full of ire. Mark Kantrowitz, in the New York Times:

He went as far as saying that the proposal could be characterized as a broken promise. “People saved money in 529 plans because of the expectation that the favorable tax treatment would continue,” he said.

But why does the New York Times let Mark Kantrowitz say this when it’s plainly not true? I saved money in a 529 plan. And the favorable tax treatment for that money will continue. When I take it out, I won’t pay a dime on any capital gains.

For money I put in later, it’s another story. But so what? If something’s on sale today, nobody’s breaking a promise to me when it’s not on sale tomorrow. I guess it’s strictly true that the proposal “could be characterized as a broken promise.” But it would be better to say it “could be characterized as a broken promise by people who don’t mind characterizing things as different things.”

A broken promise would look more like a state government defaulting on money it owes the thousands of middle-class taxpayers whose pensions it mismanaged.


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Letter from my great-grandfather

Last summer when I was at my Grandma Sylvia’s house in Tucson I copied out a handwritten letter her father, Jack Sussman, had written to her and her husband.  Here it is, for safekeeping.  Misspellings from the original.  My grandfather (also named Jack) had asthma, which is why they had moved to Tucson while my great-grandparents stayed in the Bronx.

June 12, 1944

Dear Sylvia and Jack,

First of all I want to apologize for not writing to you for such a long time. The family and I are in the Best of health. I ame also interested very much in Jacks health. I Believe that it is very important he should see a doctor more often. the same applies to you. Shirley is telling me that you dont look so good. I would like to mo wath is the matter with you. Mother and I would like to se you but it is too much expense we would rather se you come here.

I wish you a happy anniversary I hope that when your lease expires Jacks Sickness should also expire. love and kisses


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