Jazz at Van Dusen

I’ve mentioned the Van Dusen botanical garden here before, but never as an arts venue. Well, there’s got to be a first time.

Tonight was the last concert in the “Jazz in Bloom” series. The stage was set up on a lawn in the garden, with the audience sprawled before it on various blankets and portable chairs. I’m not used to thinking of a jazz concert as a family outing, but there it was, all kinds of families with small children, many unpacking picnic dinners on their blankets. At least I didn’t see any attempts to start a barbecue.

It all ended up working very nicely. I was in no particularly good mood when I came in; it didn’t help that I had to move soon after the first set started because a child sitting right behind me just wouldn’t be quiet. Still, you can’t complain much when the garden looks so gorgeous in the evening light and there’s live music to top it off. Before the end of the first set my new neighbours invited me to join their picnic and we spent a good part of the evening enjoying the food and conversation. (In the extremely unlikely case they’re reading this – thanks again!)

The first act was the Cory Weeds Quartet. They play solid traditional jazz and have put out a couple of albums with titles like “Everything’s Coming Up Weeds.” But the real standout was the second band, Zapato Negro. Here they are in a clip from the Vancouver International Jazz Festival.

That’s what they do: hot Cuban and Latin rhythms, funky and clever. They shine both in their original compositions and in their arrangements of standards, including a Latin jazz rendition of a Kurt Weill piece. Yes, Kurt Weill. That’s what they said, anyway. I would have never guessed.

(Math and math-related blogging will resume in a couple of weeks – but not just yet.)

Moon

The movie, set in a not necessarily very distant future, starts with a voice-over monologue, advertisement style. You see, back in the old days we used to rely on fossil fuels for our energy. That caused smog and pollution, affecting our health and that of the planet. (We get some impressive shots of smog in Los Angeles.) Thankfully, those times are long gone. Our skies are clear, our water is fresh, and we have enough clean energy to convert deserts into farmlands. You may ask yourself, how did we get there? Part of it, the voice-over informs us, has to do with the mining of something called Helium 3 on the far side of the moon and using it as fusion fuel. The rest of the answer will be forthcoming shortly. You might not like it.

With the opening credits still running, we meet Sam Bell (Sam Rockwell), the sole operator of one such Helium 3 mining station on the moon. He’s almost at the end of a 3-year contract, the true nature of which will be revealed gradually over the course of the movie. He is not doing well. He looks pale and disheveled, he has been talking to himself, and his mental state is so fragile that he starts to experience hallucinations. Or does he see dead people?

Maenam

(Can you tell that I’m on vacation?)

Maenam is a new restaurant in Kitsilano that has already started making waves with its innovative and sophisticated Thai cuisine. It opened just a few weeks ago to enthusiastic reviews:

If [...] you are the least bit curious about the pungent taste of rarely found holy basil, the mouth-popping sensation that occurs when you bite into the bitter shell of a berry-sized pea eggplant or the bracing vibrancy of a perfectly balanced grilled prawn salad, I highly recommend this new Kitsilano restaurant that promises to revolutionize Thai food in much the same way that Vij’s changed everything we thought we knew about Indian.

Sure enough, just as our party of 3 was finishing dinner there last week, Vikram Vij walked in, chatted with some people in the doorway, then took a place at the bar. We didn’t stay long enough to see what he was having, and didn’t have a chance to ask what he thought, but based on our experience the comparison is well enough justified. We had green papaya salad, Thai sausage, crispy pork belly with green peppercorns and a red duck curry (hope that I’m getting it right), all of which were absolutely delicious. Unfortunately I didn’t have my camera with me and couldn’t take photos of food. Then again, it’s not really the photos that you’ll want.

Maanam

My favourite Salman Rushdie novel is The Ground Beneath Her Feet. If that ever gets made into a movie, this is what Vina and Ormus should look like. That’s how I always see them.

Yes, I know that several things would be wrong with that picture, starting with the ethnicity. Still, this particular clip comes as close to it as anything I know.

An update on differentiation theorems

Malabika Pramanik and I have just uploaded to the arXiv the revised version of our paper on differentiation theorems. The new version is also available from my web page.

Here’s what happened. In the first version, we proved our restricted maximal estimates (with the dilation parameter restricted to a single scale) for all ; unfortunately our scaling analysis worked only for , therefore our unrestricted maximal estimates and differentiation theorems were only valid in that range. However, just a few days after we posted the paper, Andreas Seeger sent us a “bootstrapping” scaling argument that works for between 1 and 2. With Andreas’s kind permission, this is now included in the new version. The updated maximal theorem is as follows.

Theorem 1. There is a decreasing sequence of sets with the following properties:

• each is a disjoint union of finitely many intervals,
• as ,
• the densities converge to a weak limit ,
• the maximal operators

  

  and

  

  are bounded on for .

Our differentiation theorem has been adjusted accordingly.

Theorem 2. Let and be given by Theorem 1. Then the family differentiates for all , in the sense that for every we have

for a.e.

Furthermore,

for a.e.

What about ? I had the good luck of meeting David Preiss in Barcelona right after Malabika and I had finished the first version of the preprint. I explained our work; we also spent some time speculating on whether such results could be true in . Next day, David sent me a short proof that our Theorem 2 cannot hold with for any singular measure supported away from 0. (The same goes for sequences of sets as above, by a slight modification of his argument.) We are grateful to David for letting us include his proof in the new version of our paper.

We have also polished up the exposition, fixed up the typos and minor errors, etc. One other thing we have added (to the arXiv preprint – we are not including this in the version we are submitting for publication) is a short section on how to modify our construction of so that the limiting set would also be a Salem set. The argument is very similar to the construction in our earlier paper on arithmetic progressions, so we only sketch it very briefly.

I’ll be on vacation throughout the rest of July. I’ll continue to show up here on this blog – I might actually write here more often – and I’ll finish up a couple of minor commitments, but you should not expect any more serious mathematics from me in the next few weeks.

On every cloud a magic charm she sees

In the words of General MacArthur said, “We are not retreating. We are advancing in another direction”.

Well. Dyzma's closing speech was shorter and more to the point.

Update: For the correct attribution and context of that quotation, see here. Also, fixed the broken link.

File under: unexpected sights

I’m back in Vancouver, trying to finish up the revised version of the paper with Malabika Pramanik on differentiation theorems. There have been a couple of developments since the preprint was posted on the arXiv and we have included these in the new version. More on that soon, hopefully before the end of this week.

Meanwhile, here are a few more photos from my trip to Spain, mostly on the odd side. The first one is from the Campo del Moro gardens in Madrid. With all due respect to Nassim Taleb…

This is a small cafe in Barcelona, near Plaza de Catalunya.

The next three were taken at the Madrid-Atocha train station.

Conferences, peer review, and political interference

Our science minister Gary Goodyear is getting involved with organization and funding of scientific conferences. Last week he asked the Social Sciences and Humanities Research Council to reconsider funding for an upcoming conference at York University. Specifically, he recommended conducting a “second peer review”. Here is an excerpt from his official statement:

It has come to my attention that following a recommendation of a peer review board earlier this year, the Social Sciences and Humanities Research Council provided $19,750 under its Aid to Research Workshops and Conferences Program to a conference at York University entitled “Israel/Palestine: mapping models of statehood and prospects for peace”.

Approval of this funding was based on an initial proposal that did not include detailed information on the speakers at the conference. Since funding was provided, the organizers of the conference have added a number of speakers to their agenda.

Several individuals and organizations have expressed their grave concerns that some of the speakers have, in the past, made comments that have been seen to be anti-Israeli and anti-Semitic. Some have also expressed concerns that the event is no longer an academic research-focussed [sic] event.

The SSHRC did request an update from the conference organizers, then issued a statement to the effect that everything is in fine order, thank you very much, and the conference will be funded as planned.

The Canadian Association of University Teachers has called on Goodyear to step down:

“It’s unprecedented for a minister – let alone a minister from the department that funds the granting councils – to intervene personally with a granting council president to suggest that he review funding for an academic conference,” said CAUT executive director James Turk. “This kind of direct political interference in a funding decision made through an independent, peer-reviewed process is unacceptable and sets a very dangerous precedent.”

This blog is not an appropriate venue to discuss the Israeli-Palestinian situation, for more reasons than I could list here (and please keep that in mind if you would like to comment). Neither do I want to discuss the “hate speech” accusations such as those quoted in this article. The conference abstracts are over here. If any of them qualify as hate speech under Canadian law (see here), then there are appropriate procedures in place. Intimidation by political interference in the peer review process isn’t one of them.

I do want to repeat what I said in an earlier post: that academic freedom applies to all views expressed in the context of academic dialogue, including those we disagree with. Especially those we disagree with. That’s pretty much the point of it. And ultimately, academic freedom leads to better science. The correctness and significance of scientific ideas isn’t always clear right away and we’re better off if all such ideas are allowed to compete on their merits.

Of course, if an academic conference became a political event instead, then that would be a problem. However, a political science conference does not become a political event just because opinions about politics are being expressed. After all, that’s what political scientists do for a living. Political action – now that would be another matter. I don’t think, though, that we’ve seen any evidence of that.

But the main purpose of this post is to clarify several aspects of the organization and funding of academic conferences for those readers who have never been involved with that.

La Sagrada Familia and the hyperbolic paraboloid

I’m travelling in Spain this month – mostly for mathematical reasons, but, well, it’s Spain. Last week I was fortunate to see La Sagrada Familia.

La Sagrada Familia is the opus magnum of the great Catalan architect and artist Antoni Gaudí. Gaudí was named to be in charge of the project in 1883, at the age of 31, and continued in that role for the rest of his life. From 1914 until his death in 1926 he worked exclusively on the iconic temple, abandoning all other projects and living in a workshop on site.

The construction is still in progress and expected to continue for at least another 20-30 years. The cranes and scaffolding enveloping the temple have almost become an integral part of it. That’s not exactly surprising, given the scale and complexity of the project together with the level of attention to detail that’s evident at every step. Almost every stone is carved separately according to different specifications. Here, for example, is the gorgeous Nativity portal. (Click on the photos for somewhat larger images.)

To call Gaudí’s work unconventional would be a major understatement. To call it novelty – don’t even think about it. His buildings are organic and coherent. Everything about them is thought out, reinvented and then put back together, from the overall plan to the layout of the interior, the design of each room, the furnishings, down to such details as the shape of the railings or the window shutters with little moving flaps to allow ventilation.

Gaudí’s inspiration came from many sources, including nature, philosophy, art and literature, and mathematics.

Maximal estimates and differentiation theorems for sparse sets

Malabika Pramanik and I have just uploaded to the arXiv our paper Maximal operators and differentiation theorems for sparse sets. You can also download the PDF file from my web page.

The main result is as follows.

Theorem 1. There is a decreasing sequence of sets with the following properties:

• each is a disjoint union of finitely many intervals,
• as ,
• the densities converge to a weak limit ,
• the maximal operators

  

  and

  

  are bounded on for .

It turns out that the set does not even have to have Hausdorff dimension 1 – our current methods allow us to construct so that can have any dimension greater than 2/3. We also have $L^p\to L^q$ estimates as well as improvements in the range of exponents for the “restricted” maximal operators with . See the preprint for details.

Theorem 1 allows us to prove a differentiation theorem for sparse sets, conjectured by Aversa and Preiss in the 1990s (see this post for a longer discussion).

Theorem 2. There is a sequence of compact sets of positive measure with such that differentiates . More explicitly, for every we have

for a.e.