A physicist attends JMM

The Joint Mathematics Meetings (JMM) are advertised as the world's largest mathematics conference. This year's meeting was held in San Diego, CA, last week. DTLR attended despite his mild allergy to pure mathematics. This was my first time attending JMM, and I chose the sessions I attended with great care, and learned a lot. Some highlights are discussed below.

San Diego Convention Center, site of JMM 2018.

Physics

The best talk given by a mathematician was a physics talk, “Toy models,” by Stanford professor Tadashi Tokieda. He used a series of toys exhibiting unexpected, puzzling, and surprising behavior to illustrate ideas in physics, using almost no mathematics at all. Rather, he relied on qualitative reasoning and dimensional analysis rather than direct computation. After I returned home I discovered that many of his examples, and others, can be found in his Youtube videos, some of which are collected here. He was an exceedingly entertaining speaker – I was not bored for even one second. I would rate this as the best talk of the conference.

Computer scientist Dana Randall (Georgia Tech) gave a presentation on statistical physics, “Emergent phenomena in random structures and algorithms.” She discussed phase transitions in lattice gases, randomized algorithms, and swarm robotics, among other topics. (Phase transitions were also one of the topics addressed by Tokieda.)

Fluid Dynamics

Edriss S. Titi (Texas A&M and Weizmann Institute) provided a review of mathematical results on existence, uniqueness, and regularity of solutions for the incompressible Euler and Navier-Stokes equations under various conditions, such as 2D vs. 3D flows, and types of initial conditions. This is of course the subject of one of the million dollar prizes offered by the Clay Mathematics Institute. Rayleigh-Benard convection was given as an example. 

Isabelle Gallagher (University of Paris Diderot) presented a review of mathematical results connecting the Newton hard-sphere gas model to the Boltzmann transport equation from the kinetic theory of gases, and to the Navier-Stokes equations for a continuum fluid. One of the puzzles is how does a fundamentally reversible system – Newton's laws applied to a gas of hard spheres – result in irreversible behavior characterized by the second law of thermodynamics (reflected in both the Boltzmann and Navier-Stokes models). Her answer to this is the Ehrenfest experiment, where such a gas begins in one chamber, and at a certain time the portal to a second chamber is opened. Eventually an equilibrium is reached where both chambers have approximately the same number of particles. The key is the number of particles. If there are just two particles, nothing remarkable is observed. However, when there are many particles, the most likely states of the system are those near the equilibrium state. Thus, the statistical properties of a completely deterministic system are consistent with the second law of thermodynamics. We might think of this as an emergent behavior, not unlike those discussed in Dana Randall's talk.

Data Analysis

Topologist Gunnar Carlson (Stanford) discussed “Topological Modeling of Complex Data”. Here the “model” is not a statistical model, but rather a network model that attempts to capture the shape of data. The idea is to apply overlapping bins to the data along some of the predictor variables, and cluster the data along these axes into nodes. Nodes with overlapping data are connected, forming a network graph.

Applied mathematician Tamara G. Kolda (Sandia National Labs) spoke about tensor decompositions, particularly a decomposition known as CP (canonical polyadic). These tensor decompositions are not  orthogonal, but the idea is to essentially project high dimensional data onto what I will call basis tensors. Randomization plays a key role in the algorithm.

Neither of these presentations is by a statistician, and neither addresses statistical inference, rightly so in my view. Rather, they belong to exploratory data analysis (EDA), a field that Carlson reminds us was invented by (topologist) John Tukey.

Computer Science

Harvard computer scientist Cynthia Dwork (joint appointment with Microsoft) presented a talk on differential privacy. Algorithms that exhibit differential privacy are randomized algorithms that respond to a query to a data base, and provide the following guarantee. A specific person's decision to be included (or not) in the data base should not affect the outputs of the algorithm. Let two data sets differ by a single individual's record (she is present in one data set, and a different randomly sampled person from the population replaces her in the second). Any outcome output from the algorithm run on either data set will be almost equally likely. Algorithms with the differential privacy property are also inherently robust in the statistical sense, and can be used for adaptive/exploratory reuse of the data for statistical modeling.

A theme is evident: the talks by Randall, Kolda, and Dwork all involve randomized algorithms in computer science, not a topic that I thought about when I was a student 20 or so years ago.

What about Math?

I did attempt to attend some actual pure math talks: Alissa Crans (Loyola Marymount University) on “Quintessential quandle queries” and Craig Huneke (Virginia) on “How complicated are polynomials in many variables”. I had not heard of quandles before; the speaker related them to both groups and knots. An application to cryptography was mentioned but not dwelled on. She did at least bring a prop (a giant tetrahedron) that she used for illustration. No applications were mentioned at all in the polynomial talk, which focused on something called Stillman's conjecture. I also attended a talk by a distinguished historian of mathematics, Joseph Dauben (CUNY), on the history of Chinese math (actually, the history of Chinese historians of mathematics).

A slide from Alissa Crans' lecture on quandles, showing the definition and the mathematician who coined the term.

I also attended a panel session on careers in business, industry, and government, which probably could have run longer than it did. I was pleased to see a high level of interest in this session, but sad that many math students aren't sure how or even whether to pursue such careers. It's a good thing that they came to this session, but their home departments should be doing more to stimulate interest and provide practical resources for such career development. There was also a talk by applied mathematician Stephen Hobbs (Space and Naval Warfare Systems Center) on a simple model for deploying aircraft-carrier based resources in a humanitarian aid scenario. Finally I attended a few sessions on statistical education, including one on developing a data science program within a mathematics department.

The exhibit hall was a delight, with many book and software vendors offering their wares.  The National Security Agency had a recruiting booth which featured an original Enigma encryption device, which attendees were invited to interact with (unlike museum pieces that remain behind glass).

An original ENIGMA device at the NSA booth.

Of course, San Diego is a nice spot to go in the winter, with many extracurricular delights.

Beef empanadas at a Spanish restaurant, Cafe Sevilla, in the Gaslamp District of San Diego.