The French can retire at 62. Or 52. Sometimes 42. President Emmanuel Macron calls the tangle unsustainable. A million protesters disagree.

In the actual article, we learn that the retirement age of 42 applies to one group of workers; dancers in the national ballet. I find it very annoying when an article is teased with a number presented as normal when it’s actually extremely atypical. You could write the same teaser about the United States, having New York City firefighters in mind. But you would be misleading your audience even though the claim would be, I suppose, technically correct.

]]>So this week I tried something new, borrowing a technique I learned a long time ago for perfect sauteed asparagus. Put your butter in the pan, melt it, get those carrots sauteing in there. Put in some salt and whatever other seasoning you want at whatever time suits that seasoning. (Dill is traditional, I used nutmeg this week and it was great) Saute the carrots until they’re nicely browned. At this point *they will not be cooked enough*. Eat one, it’ll taste nice on the outside but still be crunchy and part-raw.

So now it’s time to shock the carrots. Fill a small drinking glass half-full with water. So maybe a quarter cup, I dunno. Throw the water in the hot pan and immediately, as the sizzle kicks in and the steam begins to rise, slam the lid on. It should sound sort of like a high hat when you crash and then right away mute. Turn the heat down and let the carrots steam in there for about six minutes. When you open it, the water should be gone but if it’s not I would just take the carrots out with a slotted spoon. Result: fully tender carrots that taste sauteed, not boiled.

]]>Suppose you have a sheaf F on a space, and the space has a covering U_1, .. U_N. The sheaf axiom says that if we have a family of sections s_i of F(U_i) such that s_i and s_j agree on for all i,j, then there is actually a global section s in F(X) which restricts to each s_i.

What if we only have an *approximate* section? That is: what if we have a family of s_i such that: if I select i and j uniformly at random, the probability that s_i and s_j agree on is bounded below by some p > 0. Call such a family a “p-section.” (You should take the view that this is really a family of problems with X changing and N growing, so that when I say p > 0 the content is that p is bounded away from some 0 uniformly in X,N.)

The question is then: **Is an approximate section approximately a section?**

(This is meant to recall the principle from additive number theory that *an approximate subgroup is approximately a subgroup*, as in e.g. Freiman-Rusza.)

That is: if s_1, .. s_N from a p-section, is there some actual section s in F(X) such that, for i chosen uniformly at random,

for some p’ depending only on p?

The case which turns out to be relevant to complexity theory is the Grassmann graph, which we can describe as follows: X is a k-dimensional vector space over F_2 and the U_i are the l-dimensional vector spaces for some integer l. But we do something slightly weird (which is what makes it the Grassmann graph, not the Grassmann simplicial complex) and declare that the only nonempty intersections are those where has dimension l-1. The sheaf is the one whose sections on U_i are the linear functions from U_i to F_2.

Speculation 1.7 in the linked paper is that an approximate section is approximately a section. This turns out not to be true! Because there are large sets of U_i whose intersection with the rest of X is smaller than you might expect. This makes sense: if X is a space which is connected but which is “almost a disjoint union of X_1 and X_2,” i.e. and $\latex X_1 \cap X_2$ involves very few of the U_i, then by choosing a section of F(X_1) and a section of F(X_2) independently you can get an approximate section which is unlikely to be approximated by any actual global section.

But the good news is that, in the case at hand, that ends up being the *only* problem. Khot-Minzer-Safra classify the “approximately disconnected” chunks of X (they are collections of l-dimensional subspaces containing a fixed subspace of small dimension and contained in a fixed subspace of small codimension) and show that any approximate section of F is approximated by a section on some such chunk; this is all that is needed to prove the “2-to-2 games conjecture” in complexity theory, which is their ultimate goal.

So I found all this quite striking! Do questions about approximate global sections being approximated by global sections appear elsewhere? (The question as phrased here is already a bit weird from an algebraic geometry point of view, since it seems to require that you have or impose a probability measure on your set of open patches, but maybe that’s natural in some cases?)

]]>I was in town for the always-interesting meeting of the IPAM science board. Keep an eye on their schedule; there are great workshops coming up!

There was chaos and anger at LAX when I landed, because the airport just this week moved Lyft/Uber/taxi pickups offsite. For reasons I don’t fully understand, this has led to long waits for rideshare cars. For reasons I understand even less, people are waiting an hour for their Lyft to show up when the regular taxi stand is right there, and you can — I did — just hop in a cab with no wait and go. (Yes, a VC-subsidized Lyft is cheaper than a cab, if it’s not surge time. But the bus is cheaper still, and once you’re not saving time with the Lyft, what’s the point?)

So I got in my cab and went to the beach, and watched the sunset over the ocean. Clear view of a really nice Moon-Jupiter conjunction and Venus still visible down at the horizon. Last time I went to Dockweiler Beach I was all alone, but this time there were several groups of people in Halloween costumes around bonfires. That was probably the most Blade Runner thing about this trip and it wasn’t even November 2019 yet!

I have a first cousin in LA, and good luck for me — my first cousin’s first baby was born my first morning in town! So on Saturday after the meeting I got to go see my first cousin once removed on his second day alive. I haven’t seen a one-day-old baby in a really long time! And it’s true what they say; I both remember my own kids being that age and I don’t. It’s more like I remember remembering it. I thought I was going to have a lot of advice but mostly all I had to say to them was that they are going to be amazing parents, because they are.

The hospital was in East Hollywood, a neighborhood I don’t know at all. Walking around afterwards, I saw a sign for an art-food festival in a park, so I walked up the hill into the park, where there wasn’t really an art-food festival, but there was a great Frank Lloyd Wright mansion I’d never heard of, Hollyhock House:

As with most FLW houses, there’s a lot more to it than you can see in the picture. A lot of it is just the pleasurable three-dimensional superimposition of rectangular parallelipipeds, and that doesn’t project well onto the plane.

There were a lot of folks sitting on blankets on the hillside, even though there was no art-food festival, because it turns out Barnsdall Park is where you and your 20-something moderately hipster friends go to watch the sunset in LA (unless it’s Halloween, in which case I guess you dress up and build a bonfire on Dockweiler Beach.) Sunset:

Then I ate some Filipino food, since Filipino restaurants sadly don’t exist in Madison right now, and went back to my hotel and read MathJobs files.

My Lyft driver on the way back was a 27-year-old guy from Florida who’s working on an album. That’s no surprise; my Lyft driver yesterday was also working on an album. Your Lyft driver in LA, unless they are a comic, is *always* working on an album. (My Lyft driver yesterday was also a comic.) This ride was a little deeper, though. This guy was a first-generation college student who went to school out-of-state on a soccer scholarship, majored in biology, and thought about getting a Ph.D. but was too stressed out about the GRE. He said whenever he started studying for the math part he was troubled by deep questions about foundations. Pi, he asked me: what *is* it? How can anyone really know it goes on forever? For that matter, what about two? Why is there such a thing as two? He also wanted to be a perfusionist but sat in on an open-heart surgery and decided it wasn’t for him, not in the long term. He started asking himself: is biology what I *really* want to do? So he’s driving a Lyft and working on his album. He also told me about how he doubts he’ll be able to make a long-term relationship work because he doesn’t believe in sex before marriage (he said: “out of wedlock”) and how he had dabbled in Hasidic Judiasm and how he was surprised I was Jewish because I didn’t look it (“no offense.”) Anyway, it just made me think about how normal and maybe universal his existential doubts and worries are for a 27-year-old dude; but for an upper-middle-class 27-year-old dude from an elite educational background, those existential doubts and worries would be something to process *while* you continued climbing on up that staircase to a stable professional career. That would just be a given. For this guy, the world said “You’re not sure you want that? Fine, don’t have it.”

Now I’m in LAX about to go get on the flight home to Madison, the direct flight we so gloriously now have. The last time I was in this LAX breakfast place, there was a big tumult around somebody else eating there and I realized it must be a celebrity, but I didn’t recognize him *at all*, and it turned out it was Gene Simmons. In LA people know what Gene Simmons looks like without the Kiss makeup! I do not. For all I know he could be in here right now. Are you here, Gene Simmons?

Washington University in St. Louis is hiring two new Lecturers this year: one in math, and one in statistics. These are long-term teaching-track positions, meaning they’re intended to be permanent but do not come with the possibility of tenure. I’m currently a Lecturer here, and I enjoy it a lot. I get to teach a lot of interesting courses; so far, my 3-3 load has usually included two sections of calculus and one upper-division course, with the latter including everything from probability to number theory. I also support the department’s broader undergraduate teaching mission. For example, since arriving, I’ve worked on a project to streamline the course requirements for our math major, tried out new ideas for calculus recitations, and conducted teaching interviews for postdoctoral candidates. Most importantly, my colleagues have been wonderfully supportive as I adjust to the university, try out new teaching methods and techniques in my courses, and work on departmental projects.

These teaching-track faculty positions seem to be increasingly popular, though the nature and details of such positions vary from department to department. While non-tenured, my position is on a parallel promotion ladder from Lecturer to Senior Lecturer to Teaching Professor. This structure is fairly typical, though the titles vary (Assistant/Associate/Full Professor of Instruction is also common). In our case, the promotions also come with increased guarantees of job security.

Teaching-focused positions are sometimes stereotyped as a lesser option, perhaps even a backup plan for those who can’t find a research postdoc or tenure-track job. I disagree; I see this as a good path for mathematicians who, like me, have a genuine interest in teaching and want to make it the focus of their careers. Our department and college are clear about the value they place on teaching-track faculty, too; we vote in department meetings, serve on important committees, and are treated as equals in just about every way. (The only thing we can’t do is vote on tenure-track hiring and promotion.)

Overall, I really like it here. I’m happy with my decision to pursue a teaching career, and I’m glad there are other mathematicians out there who are interested in doing the same. I would encourage such people to apply for our position and others like it. If you’re a grad student, by the way, there are teaching-focused postdoc positions too!

]]>is itself a morally problematic, even questionable, act.

Are there no editors anymore? What work is “even questionable” doing? Is it possible to imagine an act that was morally problematic but not morally questionable? And even if it is, is that thin distinction really what the writer of this piece about an HBO miniseries is going for? Or did they just think “is itself a morally problematic act” didn’t have enough heft, stuff another couple of non-nutritive words in there, admire the sentence’s new bulk, move on?

Boo, I say, boo.

]]>Anyway, Staub put together 17.4 WAR in his three seasons in Montreal and 13.1 more in 6 years with the Astros. Good satisfyingly balanced answer this year.

If you restrict to players who played for the *Nationals*, not their Quebecois predecessors, the pickings are a lot slimmer. Looks like Justin Maxwell and Mark Melancon are the best bets. I guess I give the edge to Maxwell just because he played multiple seasons for each team.

I like the weird zones of apparent order here. Of course you can do this for any planar domain, any finite set of moves, etc. Are games like this analyzable at all?

I guess you could go a little further and compute the nimber or Grundy value associated to each starting position. You get:

What to make of this?

Here’s some hacky code, it’s simple.

M = 1000 def Crossed(a,b): return (a**2 + b**2 >= M*M) def Mex(L): return min([i for i in range(5) if not (i in L)]) L = np.zeros((M+2,M+2)) for a in reversed(range(M+2)): for b in reversed(range(M+2)): if Crossed(a,b): L[a,b] = 0 else: L[a,b] = Mex([L[a+1,b],L[a,b+1],L[a+1,b+1]]) plt.imshow(L,interpolation='none',origin='lower') plt.show()

One natural question: what proportion of positions inside the quarter-circle are first-player wins? Heuristically: if you imagine the value of positions as Bernoulli variables with parameter p, the value at my current position is 0 if and only if all three of the moves available to me have value 1. So you might expect (1-p) = p^3. This has a root at about 0.68. It does look to me like the proportion of winning positions is converging, but it seems to be converging to something closer to 0.71. Why?

By the way, the game is still interesting (but I’ll bet more directly analyzable) even if the only moves are “go up one” and “go right one”! Here’s the plot of winning and losing values in that case:

]]>- Seedless watermelon cut in cubical or oblong chunks, as sweet as possible
- Good chevre (not feta, chevre) ripped up into modest pieces
- Some kind of not-too-bitter greens (I’ve been using arugula, they used some kind of micro watercressy kind of deal) Not a ton; this is a watermelon salad with some greens in it for color and accent, not a green salad.
- Roasted pine nuts (I am thinking this could also be good with roasted pepitas but have not tried it)
- Juice of a lime
- Olive oil, the best you have
- Piment d’espelette

I had never heard of piment d’espelette! It’s from the Basque part of France and is roughly in the paprika family but it’s different. I went to a spice store before I left Paris and bought a jar to bring home. So now I have something I thought my kitchen would never be able to boast: a spice Penzey’s doesn’t sell.

Anyway, the recipe is: put all that stuff in a bowl and mix it up. Or ideally put everything except the chevre in and mix it up and then strew the chevre on the top. Festive!

Of course the concept of watermelon and goat cheese as a summer salad is standard; but this is a lot better than any version of this I’ve had before.

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