Scientific

Math provides us with mental tools of incredible power. When we learn math we learn to see patterns, to think logically and systematically, to draw analogies, to perceive risk, to understand cause and effect--among many other critical skills.

Yet we tolerate and in fact expect a vast performance gap in math among students and live in a world where many adults aren't equipped with these crucial tools. This learning gap is unnecessary, dangerous and tragic, and it has led us to a problem of intellectual poverty which is apparent everywhere--in fake news, political turmoil, floundering economies, even in erroneous medical diagnoses.

The study of math is an ideal starting point to break down social inequality and empower individuals to build a smarter, kinder, more equitable world. In this talk Mighton will share his vision for a numerate society for all, not just a chosen few.

Speaker Biography

Dr. John Mighton is a playwright turned mathematician and author who founded JUMP Math as a charity in 2001. His work in fostering numeracy and in building children's self-confidence through success in math has been widely recognized. He has been named a Schwab Foundation Social Entrepreneur of the Year, an Ernst & Young Social Entrepreneur of the Year for Canada, an Ashoka Fellow, an Officer of the Order of Canada, and has received five honorary doctorates. John is also the recipient of the 10th Annual Egerton Ryerson Award for Dedication to Public Education.

John developed JUMP Math to address both the tragedy of low expectations for students and that of math anxiety in teachers. John began tutoring children in math as a financially-struggling playwright, and his success in helping students achieve levels of success that teachers and parents had thought impossible fueled his belief that everyone has great untapped potential.

The experience of repeatedly witnessing the heart-breaking paradox of high potential and low achievement led him to conclude that the widely-held assumption that mathematical talent is a rare genetic gift has created a self-fulfilling prophecy of low achievement. A generally high level of math anxiety among many elementary school teachers, itself an outcome of that belief system, creates an additional challenge.
John had to overcome his own "massive math anxiety" before making the decision to earn a Ph.D. in Mathematics at the University of Toronto. He was later awarded an NSERC Fellowship for postdoctoral research in knot and graph theory. He is currently a Fellow of the Fields Institute for Research in Mathematical Sciences and has taught mathematics at the University of Toronto. He has also lectured in philosophy at McMaster University, where he received a master’s degree in philosophy.

His plays have been performed around the world and he is the recipient of several national awards for theatre, including two Governor General’s Awards. He played the role of Tom in the film Good Will Hunting.

Systemic chemotherapy is one of the main anticancer treatments used for most kinds of clinically diagnosed tumors. However, the efficacy of these drugs can be hampered by the physical attributes of the tumor tissue, such as tortuous vasculature, dense and fibrous extracellular matrix, irregular cellular architecture, metabolic gradients, and non-uniform expression of the cell membrane receptors. This can impede the transport of therapeutic agents to tumor cells in quantities sufficient to exert the desired effect. In addition, tumor microenvironments undergo dynamic spatio-temporal changes during treatment, which can also obstruct the observed drug efficacy. To examine ways to improve drug delivery on a cell-to-tissue scale (single-cell pharmacology), we developed the microscale pharmacokinetics/pharmacodynamics modeling framework “microPKPD”. I will present how this framework can be used to design optimal schedules for various treatments and to investigate the development of drug-induced resistance.

We study the problem of classifying stationary measures and orbit closures for non-abelian action on surfaces. Using a result of Brown and Rodriguez Hertz, we show that under a certain average growth condition, the orbit closures are either finite or dense. Moreover, every infinite orbit equidistributes on the surface. This is analogous to the results of Benoist-Quint and Eskin-Lindenstrauss in the homogeneous setting, and the result of Eskin-Mirzakhani in the setting of moduli spaces of translation surfaces.

We then consider the problem of verifying this growth condition in concrete settings. In particular, we apply the theorem to two settings, namely discrete perturbations of the standard map and the \Out(F_2)-action on a certain character variety. We verify the growth condition analytically in the former setting, and verify numerically in the latter setting.

Furstenberg proved that the horocycle flow on any compact quotient of SL(2,R) is uniquely ergodic. This has been generalized by many people. I will present a proof due to Yves Coudène, which I find elegant and can prove some of the generalizations of Furstenberg's theorem too.

There are various proofs that a transitive uniformly hyperbolic dynamical system has a unique measure of maximal entropy. I will outline a proof due to Bowen that uses the specification and expansivity properties, focusing on the example of shift spaces. If time permits, I will describe how Bowen's proof works for equilibrium states associated to nonzero potential functions.