The Ottawa Mathematics Conference has showcased the academic talent of the capital region for over 10 years. Previous Keynote speakers have been:
Mayer Alvo (University of Ottawa)
Title: The Many Facets of Correlation
Abstract: The popular Pearson correlation coefficient is used to measure the linear dependence between two random variables. Its interpretation in practice depends upon the underlying distribution of the data. In this talk, we revisit the concept of correlation and define it through the use of the ranks of the data. This avoids the reliance on the underlying distribution. We then extend the notion of rank correlation to situations where the data is partially missing. We do this by introducing the concept of compatibility. In another direction we extend rank correlation to deal with angular data. We provide some examples to illustrate the concepts.
Damien Roy (University of Ottawa)
Title: On the Values of the Exponential Function
Abstract: We know that e, pi and e^pi are transcendental numbers, meaning that they are not the roots of nonzero polynomials with integer coefficients, but what about e+pi? In this talk, we present results and conjectures about the (algebraic independence of the) values of the exponential function and discuss recent advances on the topic.
Kevin Cheung (Carleton University)
Title: How Much do you Trust Computed Results?
Abstract: Mathematical software is used by mathematicians and non-mathematicians alike. Computations are used in practical applications as well as in establishing theoretical results. An example of the latter is the Four Colour Theorem. When one delegates a large chunk of mathematical derivations to a computer, a natural question arises: How much can one trust the results? Establishing correctness of computations is an active area of research. There are two complementary points of view that one can take: one is to develop provably correct software. The other, which is the focus of this talk, is to obtain ways to verify computed answers. A brief overview of some of the ideas involved in previous work will be given. A recent effort in verifying mixed-integer linear programming results will be described. Some future research directions will be discussed.
Maia Fraser (University of Ottawa)
Title: Persistence modules: from Applied to Pure Math
Abstract: The first notions of topology were invented to solve real world problems, for example in Euler’s work in the 1700’s. Later, topology grew into an important area of Pure Math in its own right. Applications continued however and I will describe some of them, in particular the recent tool of persistent homology developed in topological data analysis. Interestingly this tool in turn can be fruitfully applied within Pure Math. I discuss some new applications, including persistence modules in symplectic geometry.
Pieter Hofstra (University of Ottawa)
Title: The Joy of Abstraction
Abstract: Mathematics comes in many different flavours, ranging from very concrete and problem-driven, to very abstract and conceptual. One possible reason for introducing abstract concepts is laziness: instead of doing similar problems or proofs over and over again (perhaps with minor variations), one tries to develop a more general theory that captures all examples of interest. Another reason is that viewing a mathematical phenomenon on the “right” level of abstraction often leads to unexpected insights or connections with other concepts. In this talk, I will explain how the language of categories is particularly suitable to drawing out the essence of mathematical ideas, and to uncover new connections between seemingly unrelated areas of mathematics.
Brett Stevens (Carleton University)
Title: Tournament design, geometry and non-linear functions
Abstract: A video game tournament is held with 64 participants playing 8 games over 8 rounds. In each round, 8 people play each game against each other and no one plays the same game twice. We would like to find a tournament schedule that maximizes the number of pairs of people who play against each other in some round and minimizes the number of pairs who play against each other more than once. We set up this optimization problem as a combinatorial design. We find various solutions built from lines and ovals in finite projective planes and highly non-linear functions over finite groups. We discuss the trade-offs between the two objectives and other properties such as symmetry. the last group of solutions has some connections to Costas arrays and cryptosystems resistant to differential cryptanalysis.
Frithjof Lutscher, University of Ottawa
Title: Cyclic dynamics between mathematics and biology
Abstract: Differential equations can be used to model how certain quantities of interest change in the short run. Mathematical qualitative analysis of such equations gives us insight about the long-term behaviour that results in the system, for example: does a system converge to equilibrium, oscillate regularly, or exhibit chaotic motion? Much of this theory is being applied to understand biological systems from within-cell mechanisms to ecosystem-scale processes. In this talk, I will present some concepts of qualitative analysis of dynamical systems applied to population ecology. I will specifically talk about mechanisms that drive population cycles, and I will highlight how mathematical and ecological research interact to create deeper understanding in both fields.
Monica Nevins, University of Ottawa
Title: Algebraic Methods in Cryptography
Abstract: One of the most exciting and unexpected discoveries of the 21st century was how to use an elementary problem in number theory to implement public-key cryptography. The resulting system, RSA, is today ubiquitous (if invisible) in our internet-connected society. The reign of RSA, however, is doomed to end. In this talk, we explore other algebraic problems that lead to implementations of public-key cryptography, in anticipation of a post-RSA world.
Alistair Savage, University of Ottawa
Title: A gentle introduction to categorification
Abstract: This will be an expository talk concerning the idea of categorification and its role in representation theory. We will begin with some very simple yet beautiful observations about how various ideas from basic algebra (monoids, groups, rings, representations etc.) can be reformulated in the language of category theory. We will then explain how this viewpoint leads to new ideas such as the “categorification” of the above-mentioned algebraic objects. We will conclude with a brief synopsis of some current active areas of research involving the categorification of quantum groups. One of the goals of this idea is to produce four-dimensional topological quantum field theories. Very little background knowledge will be assumed.
Yves Bourgault, University of Ottawa
Title: Understanding the heart – problems, models and methods
Abstract: The talk will cover the challenges and approaches associated with building mathematical models of the heart. Topics covered include how to get heart geometries from medical imaging and ways to understand the electrical and mechanical activity of the heart.
Paul Mezo, Carleton University
Title: Number theory meets harmonic analysis
Abstract: Both number theory and harmonic analysis are colossal areas in mathematics, so they overlap in more ways than one. Our modest aim is to sketch a path in each area and arrive at a particular point of overlap. In the world of number theory, our path is in the direction of modular forms. In harmonic analysis we follow representations of locally compact groups. The technical core of this talk is to explain how (cuspidal) modular forms may be converted into (automorphic) representations. In making this conversion, an immense potential for generalization becomes apparent.