Art in the life of mathematicians

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This book has been in the works for some years now, and I’m thrilled to finally have a demo copy to show you. The book will be published by the American Mathematical Society. The demo copy has been produced (impressively quickly!) by the Hungarian publisher Ab Ovo. I’m very grateful to Anna Kepes Szemerédi for envisioning this project in the first place, and for all the hard work she has put into it.

I have contributed an essay on photography. You can download it here, and here is the gallery of the photos I offered to be used in the book. The photo on the cover is also mine. I hope that this will encourage you to purchase the book when it becomes available; I’m only one out of many contributors (see the cover for the list of names), and the book format will add further value through graphic design. If you’re expecting “mathematical art” as exemplified for example by the Bridges conference, I must warn you that this is not what I do. (In the essay, I explain why.) There is some overlap with one of my blog posts from last year: the post was adapted from an earlier version of the essay, and then I used it in writing the final version.

Anna first approached me about this in late 2011. I was much less confident then, both in my photography and in my writing. I have worked on both since then. One thing I wish I’d seen before I submitted my contribution is this classic piece by Linda Nochlin on the absence of great women artists in the history of art. Here’s what she says about “the lady’s accomplishment”:

In contrast to the single-mindedness and commitment demanded of a chef d’ecole, we might set the image of the “lady painter” established by 19th century etiquette books and reinforced in the literature of the times. It is precisely the insistence upon a modest, proficient, self demeaning level of amateurism as a “suitable accomplishment” for the well brought up young woman, who naturally would want to direct her major attention to the welfare of others–family and husband–that militated, and still militates, against any real accomplishment on the part of women. It is this emphasis which transforms serious commitment to frivolous self-indulgence, busy work, or occupational therapy, and today, more than ever, in suburban bastions of the feminine mystique, tends to distort the whole notion of what art is and what kind of social role it plays.

This got me thinking back on what I wrote about photography and wondering for a moment if I might have fallen into the trap of “suitable accomplishment.” In the end, it clarified for me the distinction between the commitment to the process of getting better, and the expectation of achieving a certain level of excellence, and the expectation of gaining public acclaim. I have always been anything but unambitious. Nonetheless, I have never aimed to be a “great artist.” I am not altogether indifferent to success in art, as evidenced by this self-promotional post, but what made me pick up the camera is the pleasure I find in taking photographs. My enjoyment of it is not conditional on finding an audience, receiving public recognition, or on any presumption of greatness. Instead, it comes from trying to get better at it. The pleasure is not in taking the same photographs over and over again, but in expanding my range, improving my technique, seeking out new ideas and solutions. The seriousness of my commitment is in my engagement in the process.

I suppose that this does not make me a lady.

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ICM update: talk slides

Since a number of people asked, here are the slides from my ICM talk yesterday. I have also posted them on my preprints page. I believe the talk was recorded and the video will presumably be available from the ICM webpage. Alternatively, you can read my ICM proceedings paper for a longer version.

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Maryam Mirzakhani makes history

The IMU has just announced this year’s Fields medal winners. For the first time ever, a Fields medal has been awarded to a woman, Maryam Mirzakhani. I will have the honour of attending the ceremony this morning.

The official press release on Mirzakhani’s research is available, as are the citations for the other Fields medalists. I’d like to speak to what the selection of a female Fields medalist means to me as a woman and a mathematician. In that, I would like to paraphrase something that Melissa Harris-Perry has said about the election of President Obama. Mirzakhani’s selection does exactly nothing to convince me that women are capable of doing mathematical research at the same level as men. I have never had any doubt about that in the first place, and I have said so here many times. What I take from it instead is that we as a society, men and women alike, are becoming better at encouraging and nurturing mathematical talent in women, and more capable of recognizing excellence in women’s work. I’ve said here before that the highest level of achievement within the age limit set for the Fields medals requires a confluence of both exceptional talent and favourable circumstances. Talent must be recognized, nourished, directed in productive ways, accomplishment must be acknowledged and promoted. Among the setbacks I experience every day and hear about from other women, Mirzakhani’s award offers a reason for guarded optimism, a point of evidence that sufficient dents have been made in the many layers of glass ceilings that a woman could break through all of them to the highest level.

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The human factor

A recent Telegraph article suggests that “females, as a whole, are not hugely engaged by science.” Emphasis mine:

The problem with science is that, for all its wonders, it lacks narrative and story-line. Science (and maths) is about facts, and the laboratory testing of elements. It is not primarily about people. Women – broadly speaking – are drawn to the human factor: to story, biography, psychology and language.

This self-proclaimed people specialist keeps referring to women as “females,” the noun more often than the adjective. For instance: “Biology and nature, he suggested, will generally nudge females away from [science and engineering].” Here’s to biology, I guess. And to consistency.

Here’s one good rebuttal, with further links. This essay in particular matches a great deal of my own experience. But I also want to question the “science is not about people” line from a different angle–the one that scientists adapt enthusiastically and unquestioningly in every funding application, from individual grants with a training and/or collaborative component, to conference funding, to large institute grants. For example:

The mandate of PIMS [Pacific Institute for Mathematical Sciences] is to:

  • promote research in and applications of the mathematical sciences of the highest international caliber
  • facilitate the training of highly-qualified personnel at the graduate and postdoctoral level
  • enrich public awareness of mathematics through outreach
  • enhance the mathematical training of teachers and students in K-12
  • create mathematical partnerships with similar organizations in other countries, with a particular focus on Latin America and the Pacific Rim.

NSERC pays 1.15M per year for this, and that amount does not include provincial funding or support from participating institutions. I suppose one might argue about the precise meaning of “primarily,” but the “human factor” does not exactly seem unimportant. You could also look at the webpages of individual institute programs:

The purpose of this programme is to bring together researchers in these diverse areas of mathematics, to encourage more interaction between these fields, and to provide an opportunity for UK mathematicians to engage with an important part of the mathematical computer science community.

This is very standard language. Every conference, workshop and institute program aims to bring together researchers, encourage interactions, promote the exchange of ideas, contribute to training, engage the community. Every conference proposal and grant application emphasizes it. Every funding agency demands it. Every mathematics institute derives its very existence from this notion.

And how do women score here? In light of their natural, biologically determined talents and inclinations, surely we should be looking for women scientists in particular to manage all those human interactions, or at least to participate in them significantly? PIMS has never had a female director or deputy director. Among the more than 120 participants in the program I linked above, there are 3 that I recognize as women. There are many more such examples, more that I could ever have the time to list. Women are often underrepresented at conferences (read the comment section for testimonials), both as speakers and as organizers, and when they are represented proportionally or better, this is often framed as an affirmative action gimmick rather than genuine appreciation of their contributions.

We sing the importance of communication, interaction and connection-making at the bean counters, then ignore it in our own deliberations. We take pride in choosing conference speakers based on “scientific merit,” defined as a best paper contest with an all-male jury, even when good arguments can be made that the “human factor” should in fact count towards scientific merit. And heavens help anyone who might raise the idea of inviting more women to conferences based on their alleged skills in interpersonal communication. And I don’t see women being overrepresented among institute directors, deputy directors, or other high profile research facilitators, all positions for which women should be particularly well qualified by the virtue of biology and nature.

Consistency, indeed.

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Would a mathematician pass the Turing test?

You’ve probably seen the recent announcement that a computer passed the Turing test for the first time. The announcement was followed by a healthy round of skepticism and mockery, with transcripts of chats with “Eugene” posted on a number of websites. Among other things, it has been pointed out that introducing “Eugene” as a 13-year-old Ukrainian boy holding a conversation in English would dupe most people into giving him much more slack with regard to awkward language and deficient social graces than they might otherwise.

Well, why Ukrainian boys and not mathematicians? I didn’t get to chat with Eugene. However, here is a conversation that I might or might not have had with an internet user that we’ll call Boris. I’ll let you decide.

IL: Hi Boris. I’m Izabella Laba and I work at UBC.

BORIS: Hi Izabella, it’s nice to meet you. I’m Boris. So what classes do you teach this semester?

IL: Actually, it’s summer and I don’t teach.

BORIS: That’s very interesting. So how many students do you have?

IL: I’ve just told you I don’t teach in the summer. But tell me about your research.

BORIS: As you probably know, I work on modulated gvoorups on questable aussifolds. I have proved that if a modulated gvoorup has a subquestable chain of hyperchenettes, then the aussifold must be oubliettable. This links several areas of mathematics and should have implications for the rapidly developing field of quasialgebraic oubliettability. You can read my papers to learn more about this interesting and exciting area of research.

IL: That sounds fascinating. What is a gvoorup?

BORIS: You can read my papers to learn more about it.

IL: … OK. But can you tell me why you are interested in gvoorups?

BORIS: It is a very interesting and exciting area of research. So what do you work on?

IL: Well, harmonic analysis on fractal sets.

BORIS: It is a very difficult area of research in which it is very difficult to have any new ideas.

IL: How do you know that?

BORIS: This is well known to everyone in the field, even if it has never been published. So who do you work with?

IL: Uhm, I’ve been a full professor for some time now. Are you assuming that I’m a junior researcher because I’m a woman?

BORIS: Women are more interested in teaching than in research. If you’re looking for more women, you should go to a teaching related forum.

IL: I’m pretty sure I’m more interested in research than in teaching.

BORIS: That’s great. So what classes do you teach this semester?

IL: You’re repeating yourself. I’ve answered this already.

BORIS: That’s very interesting. Have you seen my paper on gvoorups from 1995? It may be relevant to your work.

IL: Honestly, I doubt it.

BORIS: It’s been nice meeting you. Please let me know if you have any questions about my paper.

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Goldenchain trees

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by | June 1, 2014 · 8:51 am

ICM paper: Harmonic analysis on fractal sets

Somewhat belatedly, here’s the expository paper I wrote for the ICM Proceedings: a short overview of my work with Malabika Pramanik, Vincent Chan and Kyle Hambrook on harmonic analytic estimates for singular measures supported on fractal sets.

The connection between Fourier-analytic properties of measures and geometric characteristics of their supports has long been a major theme in Euclidean harmonic analysis. This includes classic estimates on singular and oscillatory integrals associated with surface measures on manifolds, with ranges of exponents depending on geometric issues such as dimension, smoothness and curvature.

In the last few years, much of my research has focused on developing a similar theory for fractal measures supported on sets of possibly non-integer dimension. This includes the case of ambient dimension 1, where there are no non-trivial lower-dimensional submanifolds but many interesting fractal sets. The common thread running through this work is that, from the point of view of harmonic analysis, “randomness” for fractals is often a useful analogue of curvature for manifolds. Thus, “random” fractals (constructed through partially randomized procedures) tend to behave like curved manifolds such as spheres, whereas fractals exhibiting arithmetic structure (for instance, the middle-thirds Cantor set) behave like flat surfaces. There is a clear connection, at least on the level of ideas if not specific results, to additive combinatorics, where various notions of “randomness” and “arithmetic structure” in sets of integers play a key role.

The paper discusses three specific questions that I have worked on: restriction estimates, differentiation estimates, and Szemeredi-type results. I’ve also mentioned some open problems. At this point, I feel like we’re only started to scratch the surface here; there is much more left to do, for example optimizing the exponents in some of the estimates I’ve mentioned and, perhaps more importantly, figuring out what properties of fractal measures determine such exponents.

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