**Speaker: **Dr. Trefor Bazett

**Title:** Untangling the Mathematics of Knots

**Abstract:** Suppose you and I each tie a knot in a piece of the rope. Could you wiggle your knot with your fingers until it looked like mine without any cutting or retying the knots? If the knots were really tangled up, it might be very hard to know whether they were really the same knot or whether they were completely different knots! In this session we are going explore Knot Theory, which uses mathematical techniques that let you perform calculations on knots and ultimately decide that two knots are different.

**Bio:** Trefor is a math prof at UVic who is passionate about sharing math ideas with his students. His favourite type of math is called Topology which studies shapes the way Geometry does, but everything is all squishy and malleable as if it was made out of Play-Doh. Cool! He also loves making math videos for YouTube.

**Speaker: **Dr. Natasha Morrison

**Title: **The Four Colour Theorem

**Abstract: **How many colours do you need to be able to colour a map in such a way that no two countries sharing a border receive the same colour? In this session, we will see how this problem is related to a more general question about colouring nodes of networks, and explore strategies for determining the minimum number of colours required.

**Bio: **Natasha Morrison joined the Department of Mathematics at UVic in 2020. Before this, she spent time as a post doctoral fellow at the University of Cambridge and at Instituto Nacional de Matemática Pura e Aplicada in Rio de Janeiro, Brasil. She obtained her PhD from the University of Oxford. Natasha has a wide range of research interests, mainly in the areas of extremal and probabilistic combinatorics. Broadly speaking, these concern understanding the structure and properties of large scale networks, and how processes, such as the spread of disease or influence, behave in various settings.

**Speaker: **Dr. Jane Butterfield

**Title: **Constructive Constructions and Historical Triangles

**Abstract: **These days, geometry is often people’s first introduction to proofs, but its roots are far more practical. In this session we’ll explore three different paradigms of geometrical constructions, starting from the *Śulbasūtras* of Ancient India, moving through Euclid’s axioms, and exploring a very practical problem from medieval Baghdad with an elegantly mathematical solution.

**Bio: **Jane Butterfield studies graph theory and math education. She has successfully talked about graph theory and combinatorics to many different types of audiences and age ranges. Her PhD research was in extremal graph theory, but she also enjoys topological graph theory, Ramsey games, and pursuit games on graphs. While a graduate student at the University of Illinois in Urbana-Champaign, she received three teaching awards, including the Campus Award for Excellence in Undergraduate Teaching. She spent two years teaching calculus to talented high school students for the Math Center for Educational Programs at the University of Minnesota, and is now an Associate Teaching Professor at the University of Victoria. At UVic, she manages the Math & Stats Assistance Centre — because of the US & Canadian spelling differences, this means she has worked for both a Center and a Centre!

**Speaker: **Dr. Asmita Sodhi

**Title:** Playing a Rubik’s Cube Like a Piano: A Brief Introduction to Group Theory

**Abstract:** What does a Rubik’s Cube have in common with chords on a piano? Mathematical structure! In pure mathematics, “algebra” isn’t about solving for *x* — it is the structure of algebraic structures and the patterns within them. We’ll look at one of these structures, called a *group*, and learn about its properties by playing with shapes and numbers. No Rubik’s Cube-solving or piano-playing skills necessary!

**Bio:** Asmita Sodhi is a math professor at UVic whose main mathematical interests are math education and number theory. She is a displaced East Coaster and obtained her PhD from Dalhousie University in Halifax, NS in 2020, which was about integer-valued polynomials (polynomials where if you input any integer, you output an integer). After completing her PhD, Asmita taught at Dal for two years before joining UVic. She is also very passionate about math outreach, and is one of the organizers of a monthly online Math Circle with the Julia Robinson Math Festival.

**Speaker: **Dr. Chris Eagle

**Title:** Hercules and the Hydra: How to Count Past Infinity.

**Abstract:** When I tell my son “I love you infinity” he tells me “I love you infinity plus one!”. Does that make any sense? In this session, we will see how to make mathematical sense out of “infinity plus one”, “infinity plus infinity”, and more. As an illustration of how counting past infinity can be useful, even in solving problems about finite objects, we will play a game involving a battle between the hero Hercules and the monstrous Hydra.

**Bio:** Chris Eagle’s background is in both mathematics and philosophy, a combination which lead to his fascination with mathematical logic. He loves sharing wonderful and strange facts about the foundations of mathematics, especially regarding mathematical problems that are provably unsolvable, with anyone who will listen. He is particularly interested in involving undergraduate students in mathematics research.