**Dr. Jane Butterfield**

**Session Title: **Mathematical Threads

**Abstract:** In this session, we will investigate how mathematics can be used to model real problems (and projects) in fibre arts. We will look at certain types of embroidery, knitting, crochet, and more, and along the way will peek at problems in topology, coding theory, and graph theory.

**Bio:** Jane Butterfield studies graph theory and math education, and has given numerous talks on graph theory and combinatorics to many different audiences and age ranges. While her PhD research was in extremal graph theory, Jane also enjoys topological graph theory, Ramsey games, and pursuit games on graphs. 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, Jane 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!

**Dr. Natasha Morrison **

**Session 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.

**Kate Nimegeers**

**Session Title:** We like to Parti-tion

**Abstract: **In this session, we will consider the concept of integer partitions, examine their visual counterpart (Young diagrams), and explore some activities on creating standard Young Tableaux. Activities that reinforce the concepts will make up the majority of the time, including a fun photo of our group in a standard Young Tableaux, so be prepared to learn and laugh. If you pay close attention and apply what you learn to the bonus questions, you might be able to make Kate do extra exercise all week long!

**Bio: **Kate Nimegeers (she/they) is a MSc Discrete Mathematics student at UVic studying Sudoku puzzles under the supervision of Dr. Peter Dukes. In their spare time Kate likes to noodle around on the guitar, trail run, play Dungeons and Dragons, and cuddle kitties. A fun fact about Kate is that she didn’t know she even liked math until she was 24 years old! You’re never too young or too old to discover something new and wonderful in the world of mathematics!

**Dr. Chris Eagle**

**Session 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.

**Dr. Peter Dukes**

**Session Title: **Pairs vs. Triples: What’s the difference?

**Abstract: **When working with integers modulo n, we compute a sum or difference of elements with “wrap-around”; that is, integers are reduced to their remainder when divided by n. For example, in the integers modulo 7, we have the sum 4+5=2 since 9 has remainder 2 when divided by 7. The set A={1,2,4} in the integers modulo 7 has an interesting property: every nonzero element occurs exactly once as a difference between two elements of A. In 1939, Rose Peltesohn completely determined when families of triples with this property exist in the integers modulo n. In this session, we will explore Peltesohn’s work in more detail. After experimenting with some small cases, we will examine some of the beautiful geometric configurations resulting from Peltesohn’s constructions.

**Bio: **Peter Dukes received a Ph.D. in mathematics from Caltech in 2003, and joined UVic as a faculty member in 2004. Peter enjoys the interplay between combinatorics and other areas of mathematics, such as linear algebra, geometry and number theory.

**Shannon Ogden**

**Session Title:** A Mathematician’s Guide to World Domination

**Abstract:** How can one defend a vast empire with a minimal number of soldiers? This was the dilemma faced by emperor Constantine during the decline of the Roman Empire. In this session, we will attempt to avert the fall of the Roman Empire by improving upon Constantine’s defensive strategy. By representing the cities and major roads of the empire as the vertices and edges of a graph, we will model various troop deployment strategies in order to determine the minimum number of soldiers required to successfully defend the Roman Empire.

**Bio:** Shannon Ogden (she/her) is a masters student at UVic, where she studies graph theory under the supervision of Dr. Kieka Mynhardt and Dr. Natasha Morrison. As the Outreach Program Coordinator for UVic’s student chapter of the Association for Women in Mathematics, Shannon is always looking for new ways to inspire young mathematicians. She loves playing the piano (never mind how poorly) and the unequaled satisfaction of a well-organized bookcase brimming with gorgeous editions of classic novels. When not buried in math papers, Shannon can often be found rock climbing, hiking, or simply looking for the perfect tree under which to read.

**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 will explore Knot Theory, which uses mathematical techniques that let you perform calculations on knots and ultimately decide that two knots are different.

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