# Category Archives: mathematics: conferences

## Universities in the time of climate change

This is the HTML version of my submission to the Proceedings of the JHU Workshop on Professional Norms in Mathematics, organized by Emily Riehl in September 2019. I gave a (virtual) presentation there, circulated a set of slides, and was in the process of writing a longer piece based on that when life started to get in the way. Here it is now, with updates to account for recent events. I owe much gratitude to Emily for her encouragement and patience.

1. My first attempt at this essay grew out of my frustration with common institutional responses to the climate emergency. “Sustainability” has become yet another bonanza for developers and manufacturers. New energy-efficient buildings are joyfully constructed, appliances are replaced as soon as a newer and slightly more efficient model becomes available. A typical sustainability webpage boasts of new construction, fundraising, and multimillion “green” developments, with a sprinkling of low impact feel-good projects on the side: bikes, straws, reusable coffee mugs. Institutions act as if “shop more, save more” were deep words of wisdom that applied to the environment, as if we could address a crisis of uncontrolled expansion by doing more of the same. As for the employees and customers, or faculty and students, we are expected
to allow ourselves extra time for construction-related detours on our way to work, yield the right of way to heavy machinery, take a yoga class if we discover that we have anger management issues, and otherwise continue as usual.

I spoke about this, remotely, at the JHU Workshop on Professional Norms in Mathematics in September 2019. I wrote in my set of slides for the talk:

Climate change will be hard on us, both physically and mentally.
Heat waves, wildfires, air quality, disaster preparedness and responses, power outages,
boiled water advisories, etc.: we will not be able to rely consistently
on modern age conveniences.

When the slides were circulated on the internet and blogged at the Azimuth, reactions were divided. One tech person on Twitter said that this was nonsense: we would be able to shield and air-condition a university in the middle of the Death Valley if needed, this would be an obvious priority given that the future of humanity depends on the continued ability of the smartest people to work in comfort. A few weeks later, under the threat of wildfires, the California utility PG\&E cut off electricity to various locations including the Berkeley campus of the University of California.

I also wrote this:

We will not be able to demand that everyone must operate at 100% capacity, 100% of the time. Employers will have to acknowledge that people are human, and plan accordingly. If lack of resources does not stop us, public health issues will do it.

I did not know that a global pandemic was just around the corner.

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## Back from the summer school

The summer school in analysis was excellent. I was impressed by the quality of the presentations and the engagement of the participants. This was also my first visit to the beautiful island of Catalina, and while we obviously weren’t there on vacation, we did have a free afternoon to explore it.

Also, my sabbatical leave officially begins today. I have spent a good deal of time in recent years establishing the harmonic analysis group at UBC, recruiting and supervising postdocs and graduate students, organizing conferences and institute programs, and serving the community in other ways (Putnam committee, expository writing and talks). This all has been satisfying, but it also took a toll on my own research program, and it is about time to rectify that. I look forward to being able to engage fully in research over the next year.

Filed under mathematics: conferences, photography

## Photos from the CMS meeting

Nets Katz talks about the distinct distances problem. (A late addition to the Harmonic Analysis session.)

Ron Graham expects to have to write a cheque soon.

The audience looks happy.

Tamar Ziegler gives a plenary talk.

Olof Sisask is visiting me for a few months. He made it here just in time for the conference.

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## Happy Birthday, Cathleen!

This week I’m in Toronto, attending a conference dedicated to Cathleen Morawetz on her 85th birthday. Cathleen has had a long and distinguished career. She is well known both for her groundbreaking work in PDE theory (Morawetz estimates) and for her service to the community. I’m honoured to be part of her celebration.

More photos under the cut.

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## Conference update, part II

Better late than never… here’s the belated second part of the update on the Clay-Fields conference. We were very lucky to have Tim Gowers give the Distinguished Lecture Series during the conference, and in this post I will try to give a brief account of his lectures.

There were of course many other interesting talks – in fact this may have been the first time in my life that I attended every single lecture at a conference. I wish I had the time to write about them all. That won’t be happening now, but many of the conference topics are close to my research interests and it’s likely that they will come up in future posts.

This was also the first time that I was the main organizer of a conference this size. It’s been a lot of work, but it has also been very rewarding and totally worth it. I’ve had a lot of help from Andrew Granville, Bryna Kra and Trevor Wooley, and the Fields staff did a fantastic job running everything so smoothly. We’d had new audiovisual equipment installed in the conference room just days before the conference… and everything worked perfectly from day one. Isn’t that something? We even had a screening of two short experimental movies, courtesy of Andrew Granville.

Thanks again to all participants for coming!

The rest of this post will be about Tim’s lectures. It’s a little bit long, so I will put it under the cut. The subject is “quadratic Fourier analysis”.

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## Conference update, part I

Here’s a small sample of what we’ve had so far.

Before the conference even began, Vitaly Bergelson gave two introductory talks on the ergodic approach to additive number theory problems: the first one about the Poincaré recurrence theorem, the second about equidistribution, the “van der Corput trick” and Weyl differencing. While the lectures were accessible to students, they also included a good number of things that the senior mathematicians in the audience might not have heard before, from the history of the subject to a somewhat unexpected “quadratic” point of view on the theorems of Roth on arithmetic progressions and Sárközy on square differences in dense sets.

Vitaly’s conference talk started with an introduction to Szemerédi’s theorem.  (There were reportedly people in the audience who didn’t know Szemerédi’s theorem – which is great!  We’re always happy to see new people around and to introduce them to the subject.)  He then went on to discuss his work with Alexander Leibman and Randall McCutcheon on ergodic theorems and an extension of the polynomial Szemerédi theorem to “generalized polynomials” – functions that can be built by iterating polynomials and the floor function.

To continue with the ergodic theory theme – Tamar Ziegler talked about her work with Terry Tao on the polynomial Szemerédi theorem in the primes, and Bernard Host gave a lecture on his joint work with Bryna Kra on nilsequences and their applications in ergodic theory and additive combinatorics.  We have two more “ergodic” talks scheduled tomorrow, by Nikos Frantzikinakis and Maté Wierdl.

Ben Green and Terry Tao both gave talks about the progress on their program to prove the Dickson (or Hardy-Littlewood) conjecture on the asymptotic number of solutions to linear equations in the primes. In an earlier paper, they reduced the “non-degenerate” case of the conjecture to proving two statements, which they dubbed the inverse Gowers norm conjecture and the Möbius-nilsequences conjecture. (“Non-degenerate” means that the system does not either include or encode implicitly any equation in two variables.  For instance, the twin primes conjecture involves the equation $x_1-x_2=2$, which is degenerate.)

According to Terry Tao, they have now resolved the Möbius-nilsequences conjecture – this was the subject of his two lectures.  The proof consists of a “number-theoretic” part where specific information about the Möbius function is exploited via the circle method, and a “dynamical” part involving a new Ratner-type theorem for nilmanifolds.  I’m sure that we will be hearing more about this soon!

Ben Green gave an update on the inverse Gowers conjecture.  For the $U^3$ norm, this conjecture was proved by Green and Tao in 2005 in ${\bf Z}_N$ and in finite fields of characteristics $p\geq 3$, and by Samorodnitsky in characteristics 2.  Last year, Lovett-Meshulam-Samorodnitsky and (independently and about the same time) Green-Tao found finite fields counterexamples for $U^d$ norms with $d\geq 4$.  However, these examples only work in finite fields of low characteristics.  In a recent paper on distribution of polynomials over finite fields, Green and Tao proved that this particular type of counterexamples can’t occur if the characteristic of the fields is large enough; in particular there is still a good chance that the conjecture will be true in ${\bf Z}_N$.  (See Terry’s blog post on the subject.)

Akshay Venkatesh gave a “speculative” (his words) lecture about his joint work with Jordan Ellenberg on modelling number-theoretic phenomena by the statistics of seemingly unrelated random objects. For instance, the distribution of zeroes of L-functions can be modelled by the distribution of eigenvalues of random matrices chosen from a fixed subgroup of SL(N) for some large N; this goes back to Montgomery in the case of the Riemann zeta function, and to Katz-Sarnak and Cohen-Lenstra for more general L-functions. Another example: there are parallels between the statistics of arithmetic functions (e.g. partition or divisor functions) and certain phenomena in algebraic geometry. Most of this is heuristic rather than rigorous, but the numerical evidence is reported to be quite compelling and the heuristic considerations do suggest intriguing questions. In a follow-up Math Department colloquium talk, Akshay described some specific results of this type (joint with Jordan Ellenberg and Craig Westerland) at the interface of number theory, algebraic geometry and topology.

To be continued…

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## The Clay-Fields Additive Combinatorics conference

We are getting very close the largest event of the Fields thematic program: the Clay-Fields conference on Additive Combinatorics, Number Theory and Harmonic Analysis. The conference will start on the morning of Saturday, April 5 (that’s only 2 days from now) and end on Sunday, April 13, early in the afternoon.

The conference will feature over 40 speakers, ranging from the famous and distinguished (Jean Bourgain, Tim Gowers, Ben Green, Endre Szemerédi, Terry Tao, and others) to some of the best junior mathematicians in the area that we could think of. We are honoured and delighted to have such an impressive slate of lecturers.

Tim Gowers, the Rouse Ball Professor of Mathematics at Cambridge and a 1998 Fields medalist, will give the Distinguished Lecture Series during the conference. He will speak on “Quadratic Fourier Analysis”, which originated in his 1998 proof of Szemerédi’s theorem and then was pushed much further by Green and Tao, and its applications in additive number theory and additive combinatorics.

We’re planning to have no more than 5 hours of lectures per day (5 1/2 on Tuesday), so there should be ample time for discussions, collaboration, and of course social life. This also means that at the end of the day I may still have some time to post updates on the conference highlights.

The conference is co-sponsored by the Fields Institute and the Clay Mathematics Institute.  The organizers are David Ellwood (CMI), Andrew Granville, Bryna Kra, Trevor Wooley, and yours truly.

Hope to see you there!

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## Brain damage

In case you were wondering how my brain might feel after 5 rather intense days of a workshop…

There. That’s how.

It’s also one of the best music videos that I know of.