Daily Archives: January 9, 2016

Drinking from a Fire Hose: the Current Events Bulletin

Yesterday, in a feat of mathematical endurance, I attended all four talks in the Current Events Bulletin. The Current Events Bulletin, started in 2003, is a neat idea for the joint meetings: prominent researchers give expository talks about important areas of research (generally not including their own research) for a general mathematical audience. This year, Carina Curto talked about topology and the neural code, Yuval Peres talked about the dynamics of abelian sandpiles, Timothy Gowers talked about probabilistic combinatorics and recent results in combinatorial design theory, and Amie Wilkinson talked about Lyapunov exponents. All four also contributed short overview papers to a booklet available to the audience. (The booklet is also available online as a pdf.) Interestingly, each talk was about 45 minutes long with a short break halfway through to allow people to escape if necessary without causing too much commotion.

These summaries are based only on my notes from the talks. I apologize for any errors or misinterpretations.

I probably got the most out of Carina Curto’s talk both because it was the first talk, so I was not yet fatigued, and because I went in knowing almost nothing about the topic. Topology comes into neuroscience in several guises, including topological data analysis, network theory, and understanding the neural code, the way the brain encodes information. Curto focused on the last topic, particularly as it relates to information about place. Neurons called place cells fire in response to an animal’s location in its environment. Even more interesting to me are grid cells. These cells fire based on the animal’s location in the environment, but the same neuron fires in response to several locations. The locations that cause one neuron to fire form a hexagonal lattice in the environment. Topology comes into studying both place and grid cells. For place cells, the places that stimulate each neuron form an open cover of the environment. (At the phrase “open cover,” topologists instinctively prick up their ears.) By looking at the firing of the place cells, the topology of the environment can be reconstructed based only on that information. For grid cells, there is a “fundamental domain” of the environment; the grid cells respond as if the environment is a torus. Weird!

Yuval Peres spoke about sandpiles. I’ve read a little about them before, including a great Nautilus article by Jordan Ellenberg. The idea of an abeliean sandpile is that you start with a number of grains of sand on one square in a grid. When the square has four grains of sand on it, it topples over, giving one grain of sand to each neighboring grid cell. (It’s abelian because, although it is not obvious, when two squares both have 4 or more grains of sand, the order of toppling doesn’t matter.) Peres talked about this problem and variations thereof. The starting grid can be seeded instead of empty. The “sand” can be made continuous instead of discrete, so a square can keep an integer amount of sand and equally distribute a fractional amount to each neighbor (in his article about it, he appealingly described this model as maple syrup in the grid of a waffle). Then there was “rotor routing,” which encodes a “nonrandom random walk” on the grid by labeling the squares with directions as the walker walks through them. Peres included a tantalizing open question at the end of the talk. He showed us a two-dimensional sandpile and a slice of a three-dimensional one. Outside of a neighborhood of the origin, the pictures were the same. Not similar, but pixel-by-pixel identical. There is currently no proof of why that would be.

Timothy Gowers spoke about Peter Keevash’s recent work on combinatorial design theory, especially ideas of probabilistic combinatorics. The standard example question is the Kirkman schoolgirl problem. There are 15 schoolgirls, and they walk to class in five rows of three. Is there a way they can walk so that over the course of the week, no two of them walk abreast twice? The general problem is to determine whether, in a set of n people, there is any way to form groups of people so that every set of s people is contained in exactly one set of r people? Gowers introduced some naive ways to approach the topic and explained why they didn’t quite work but how some of them could be tweaked to

Amie Wilkinson’s topic was the one I was most familiar with already, although because I am familiar due to more to my spouse’s rather than my own research (I am a dynamicist-in-law), my knowledge has some gaps. Her talk title is a question I have wondered about several times: What are Lyapunov exponents, and why are they interesting? The example she started with was the successive barycentric division of an equilateral triangle. As you find the barycenters of the triangles, is there some kind of limiting triangle shape? To make this question more precise, when you take a random walk through the triangle, choosing one of the six subtriangles at each step, how does the “aspect ratio” change? In this case, it goes to zero, so the triangles are getting very thin and needlelike. The rate at which they get needle-like is the Lyapunov exponent. After explaining what they were, Wilkinson gave a general overview of some of the places they pop up in Fields medalist Artur Avila’s work: ergodic theory, translation surfaces, and 1-dimensional Schrödinger operators.

On a practical note, the talks were in a dim, warm room, and by the end of the second one, I was sore from sitting so long. But I took a deep breath and powered through. In other words, this was a professional on a closed course. Do not attempt at home.

And the Oscar Goes to…

The joint prize session is only 50 minutes long and doesn’t have a red carpet, but it is a chance for mathematicians to get together and congratulate each other for doing good math. The prize session and the AWM prize session the night before really show how varied* mathematics and the joints meetings themselves are. There are prizes for research accomplishments, research articles, expository writing, communicationservice to the profession, teaching, undergraduate research, and, if that were not enough, lifetime achievement. The recipients work on a huge range of topics in pure and applied mathematics.

AWM president Kristin Lauter congratulates my student Mackenzie Simper on the Alice T. Schafer award. Photo: Magnhild Lien.

AWM president Kristin Lauter congratulates my student Mackenzie Simper on the Alice T. Schafer award. Photo: Magnhild Lien.

The prize session recognizes a number of individuals, but reading the prize booklet and hearing their brief remarks started to make me feel warm and fuzzy. Even though we recognize them as individuals, they all seem to thank their families, their collaborators, and their students. Math is not a solo activity!

On a personal note, I can take no credit, but I am absolutely thrilled that one of my students, Mackenzie Simper, was awarded the Alice T. Schafer prize for excellence in mathematics by an undergraduate woman. I only met her last semester when she was in my complex analysis class, after she had done much of the work that would earn her the prize. Nevertheless, I can at least claim I knew her when…

You can read about all the prize awardees here (pdf).

*I originally wrote the word “diverse,” but a glance up at the stage showed a sea of white men in dark suits. There were a few people who didn’t fit that description, but I’m afraid we have a lot of work to do before I can use the word “diverse.”

A familiar story

movieposterThursday evening, I watched the MAA special screening of A Brilliant Young Mind, starring Sally Hawkins and Asa Butterfield. The movie follows a young man on the autism spectrum who finds solace in doing mathematics. His dream is to go to the International Mathematical Olympiad, and most of the movie follows this process and his training, first by an unconventional teacher in the UK, and then at a math camp in Taipei.

I enjoyed the movie, and it was well-made (shot beautifully and brilliantly scored), with incredible acting from the three main stars: Rafe Spall was very convincing as a bitter, but kind, man struggling with MS, Butterfield brought a good balance of detachment and neediness, and Hawkins is perfect in everything she does. The main message of the movie is easily summarized by its tagline: “True genius comes from opening your heart.” Most of the movie people are obsessed by external validation: the teacher wants his student to shine, the student wants an IMO medal, the mother wants her son to love her in a way he can’t. By the end, they find value in themselves. Especially Nathan Ellis, the young hero, finds connection and love with another math competitor, reconciles with his mother, and discovers that there are things far more important than being “clever”.

Overall, I do like the message. My problem is that the structure is a very well-tread upon series of events taking the young awkward boy, who is so socially awkward he can only do math, to a young man who gets a girlfriend and (maybe) stops caring about math. The implications are that math is only for those who cannot make emotional connections, and even more so awkward, white males. There are some girls in the math teams, one of whom becomes the love interest, but her role is weakened by the fact that she supposedly only makes the team because her uncle is the coach, and then decides to quit because she doesn’t believe she is good enough. The love story is very cute, but could have been connected to the math life a little better. For example, why can’t we show that you can be in young puppy-love and still like doing math? Why did the star have to be a boy, and not a girl? My main problem with the movie is that we have seen this story many times before (most notably in Good Will Hunting), and the setting, actors, and drama of the IMO could have been much better used to tell a story with the same message: that it’s important to make human connections, and that medals and recognition are not the reason to do math.

Overall it was a pleasant movie, but it could have been much better with a few tweaks. The movie comes out in DVD at the end of the month, in case you’re interested.