Mini Courses
Continuous Optimization
The maximum entropy on the mean method for linear inverse problems
Friday, November 29  1pm  4pmâ€‹
The principle of maximum entropy states that the probability distribution that best represents the current state of knowledge about a system is the one with largest entropy with respect to a given prior (data) distribution. It was first formulated in the context of statistical physics in two seminal papers by E. T. Jaynes (Physical Review, Series II. 1957), and thus constitutes an informationtheoretic manifestation of Occam’s razor. We bring the idea of maximum entropy to bear in the context of linear inverse problems: we solve for the probability measure that is close to the (learned or chosen) prior and whose expectation (mean) has small residual with respect to the observation. Duality leads to tractable, finitedimensional (dual) problems. A core tool, which we then show to be useful beyond the linear inverse problem setting, is the “MEMM functional”: it is an infimal projection of the KullbackLeibler divergence and a linear equation, which coincides with Cramer’s function (ubiquitous in the theory of large deviations) in most cases, and is paired in duality with the cumulant generating function of the prior measure.
Professor Tim Hoheisel
McGill University
The minicourse consists of two lectures:

A thorough introduction to the necessary results from convex analysis.

A brief summary of the necessary tools from measure theory followed by the abovementioned duality schemes as well as datadriven approaches to employ the MEM methodology.
Logic/Set Theory
Borel reducibility and the method of forcing
Friday, November 29  1pm  4pmâ€‹
This minicourse will introduce the theory of Borel reducibility, with particular emphasis on the study of pins for equivalence relations. Roughly speaking, pins are equivalence classes which may live in a forcing extension but can be simply defined in the base model. We will begin by covering some background on Borel reducibility and forcing, and introduce early motivations and some application of pins in the context of Vaught's conjecture, such as Harrington's theorem, Hjorth's characterization of Polish groups satisfying Vaught's conjecture on analytic sets, and the HjorthThompson characterization of Polish groups admitting a complete left invariant metric. We will then see how a more careful study of pins can be used to study equivalence relations higher up in the Borel reducibility hierarchy, and present some applications for Borel irreducibility results, following results of Larson, Laskowski, Rast, Ulrich, Zapletal.
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We will assume some basic familiarity with descriptive set theory and mathematical logic.
Assaf Shani
Concordia University
Mathematical Modelling of Traffic Flow
This course aims to introduce the audience to basics of mathematical modelling with specific applications of vehicular traffic.
Friday, November 29  9am  12pmâ€‹
Isha Dhiman
University of the Fraser Valley
Within the twenty first century, one of the problems created by the increasing population, which is of great concern today, is that of congestion. Reportedly Vancouver is one of the busiest cities in North America. In a constant effort of reducing traffic congestion in today’s overcrowded world, the field of traffic flow theory is perplexed by mixed terminologies and widely varying notations by mathematicians, physicists, traffic engineers, economists and, even, practitioners of operations research.
The main goal of traffic engineering is to plan and design efficient road networks to have a smooth transportation. Another motive is to design strategies for fast online simulations, which can be helpful in traffic forecasting and might prevent occurrence of traffic jams, which is an undesirable physical situation and can occur due to many reasons such as highvolume traffic, spatial inhomogeneities and spontaneous perturbations of traffic. An additional objective worth mentioning is the need to reduce traffic accidents, a human and social cost.
The mathematical modelling and analysis of traffic flow can provide insights into this field and other related areas as well.
We will try to cover the required fundamentals for gaining ideas about pursuing further research in this field.
The minicourse consists of three parts: