# June 19-23

### Keynote lectures ### University of Toronto

#### Title: The Dynamics of Ocean WavesAbstract: Many aspects of mathematical analysis were originally motivated by the study of fluid dynamics; in particular, waves and currents in bodies of water. I will discuss how mathematical analysis combined with asymptotic theory and accurate numerical simulations contributes, in turn, to a better understanding of the dynamics of ocean waves both at the surface of the ocean and in its interior, in regular situations and in extreme events. ### University of Toronto

#### Title: The projective plane and its relation to perspective drawingsAbstract: During the Renaissance artists figured out the visual principles of central perspective where two parallel lines seem to meet at infinity. Later mathematicians constructed the projective plane $$\mathbb P^2$$ and higher projective spaces $$\mathbb P^n$$. We will define the projective plane, explore some of its properties, and consider applications to perspective drawings. As an examples we will study one-point and two-point perspective, and also look at anamorphic art and cubism. ### University of Toronto

#### Title: How to solve cubic and quartic equations by radicals?Abstract: Everybody knows that polynomial equations of degrees three and four can be solved by radicals. But how to do it? Cardano’s formula for the roots of cubic equations is too complicated and hard to remember. Reduction of degree four equation to cubic equation also is not obvious. In the talk I will present simple solutions to the following problems. Problem 1. Assume that the cosine of an angle α is given. Find a cosine of $$\frac{\alpha}{n}$$ for a given natural n using radical.Problem 2. Solve by radicals any system of two polynomial equations of degree two in two unknowns. I will explain how solutions of these Problems imply solutions of cubic and quartic equations. I also will discuss a beautiful J.F. Ritt’s theorem (1922) on polynomial invertible by radicals and its recent generalization obtained by Yu. Burda and me. ### University of Toronto

#### Title: Five fictions of math and how they keep women out of STEM Abstract: Math is peppered with fictions, or narratives that are “invented but are still held to be true because it is expedient to do so” (Oxford dictionary). In this talk we will take a step back and critically examine mathematics as a discipline. We will investigate how several common fictions impact women individually and as a population, surveying research on math students from elementary school through graduate school and practicing mathematicians. Rather than just removing the false narratives that discourage women from pursuing math, we will go one step further to reimagine characteristics of an explicitly feminist math. ### University of Toronto

#### Title: The mathematics of sorting networks Abstract: An n-element sorting network is a way of sorting the list of numbers (1, 2, ..., n) into decreasing order by repeatedly swapping pairs of adjacent numbers that are currently in increasing order. For example, (1, 2, 3) -> (1, 3, 2) -> (3, 1, 2) -> (3, 2, 1) is a 3-element sorting network. How many n-element sorting networks are there? What happens if we choose one of these sorting networks at random? These questions lead to surprising and beautiful mathematics involving block stacking, sliding puzzles, solitaire, sine curves, and an old theorem of Archimedes. ### University of Toronto

#### Title: Modeling Mobius with randomness Abstract: The Mobius function is a classical multiplicative object in number theory and is famously related to the Riemann hypothesis. It is determined by the prime factorization of integers, which makes it notoriously difficult to understand its true behaviour. There has been exciting progress in the study of random models of the Mobius function known as 'random multiplicative functions'. I will introduce this active area of research as well as some of its accomplishments and possible future directions. ### University of Toronto

#### Title: Symmetry, Conservation, and Geometry Abstract: Symplectic geometry has its roots in physics (classical mechanics and quantum mechanics). The prototype for a symplectic structure is the classical phase space, which parametrizes the position and momentum of an object. Noether’s theorem tells us that for every symmetry of a physical system there is a conserved quantity – for example symmetry under translation gives rise to conservation of momentum. Another way to look at this is that a symmetry group (such as rotation on the surface of the earth) often gives rise to to a conserved quantity. In the case of the rotation group, the conserved quantity is angular momentum.

• Lindsey Shorser

With more abstracts to come.