**Summer 2022**

**Speaker: **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!

**Speaker: **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.

**Speaker: **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!

**Speaker: **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.

**Speaker: **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.

**Speaker: **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.

**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 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

**Fall 2022**

**Speaker:** Dr. Jane Butterfield

**Title:** Geometrical Proofs Across Cultures

**Abstract:** You might have heard that it’s impossible to square a circle, but did you know that it is also impossible to trisect an angle? What does any of that really mean, and under what circumstances is it really true? We will explore three different paradigms of geometrical constructions, starting from the Śulbasūtras of Ancient India, moving through Euclid’s axioms, and finally adding the more recent Origami axioms.

**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!

**Speaker:** Dr. Audrey Yap

**Title:** Philosophy of Mathematics

**Abstract/Bio:** I’m an Associate Professor in the philosophy department, and have worked in logic, the history and philosophy of math, and feminist philosophy. I wanted to study logic and philosophy of math in grad school mostly because I love that, in logic and math, you can actually have a right answer. The problem is, when you study too much philosophy, you start to worry about whether those answers are *really* right after all. In this session, I will talk about the philosophy of math, including some of the questions people have had over the years about what math is all about, and why we even think it works.

**Speaker:** Dr. Natalie Behague

**Title:** Un, Dos, Tres: How to Count

**Abstract:** You probably think you already know how to count. Well think again! In this hands-on session, you will be presented with some mathematical objects that are difficult to enumerate, and you will work in small groups to apply three different approaches to counting them: namely, being systematic, finding correspondences, and recursion — building bigger cases up from smaller cases. We will discuss the strengths and limitations of each approach, and with any luck there will be some insights and surprises along the way.

**Bio:** Natalie Behague is a postdoctoral research fellow at the University of Victoria. She works in various topics under the broad umbrella that is combinatorics, investigating objects including graphs (in the sense of a collection of nodes and edges between them), two-player games (think tic-tac-toe) and automata. Natalie is from the UK and was educated at the University of Cambridge and Queen Mary University of London. With terrible timing she moved to Canada in 2020, spending a year working from home for Toronto Metropolitan University before moving to Victoria in January 2022.

**Speaker:** Dr. Trefor Bazett

**Title:** The Bizarre Worlds of Non-Euclidean Geometry

**Abstract:** Straight lines, triangles, circles, these are the familiar types of objects we study in geometry. However in non-Euclidean geometry we imagine worlds where theses geometric objects behave in new and fascinating ways. For example, a ‘straight line’ drawn on a ball like the surface of the earth becomes a circle around the ball, and this is just the beginning of the weirdness! You should bring a compass for drawing circles to this session.

**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

**Speaker:** Dr. Gourab Ray

**Title:** The 100 Prisoners Problem

**Speaker:** Dr. Jon Noel

**Title:** Solving HUGE problems quickly

**Abstract:** What is the fastest way to multiply two humongous numbers? The standard multiplication method that you learned in elementary school is a great for small numbers, but what about numbers with 10,000 digits? Is there a better way? (Spoiler alert: yes, there is). In this session, we will learn about different methods (i.e. “algorithms”) for solving mathematical problems, and how to compare different algorithms to determine which one is the “fastest.”

**Bio:** Jon Noel is a math prof at UVic interested in discrete mathematics and its connections to other areas like computer science, analysis, and statistical physics. Much of his work revolves around understanding the “extreme” behaviour of very large networks. He grew up in Kamloops, BC, where he also completed his undergraduate degree from TRU in 2011. He obtained his Master’s from McGill in 2013 and PhD from the University of Oxford in 2016. Before coming to UVic, he worked in postdoctoral positions in Switzerland and the UK.

**Spring 2023**

**Speaker:** Dr. Gary MacGillivray

**Title:** Take-away games

**Abstract:** Imagine there is a pile of 101 coins on a table. Two people play a game in which they take turns removing one or two coins from the pile. The person who takes the last coin wins. Does it matter if go first or second? Using inductive reasoning it turns out to be possible to determine which player wins and their winning strategy. We’ll talk about how to use it to analyze this game, and similar games.

**Bio:** Gary MacGillivray got his BSc from UVic in 1985, his MSc from UVic in 1986, and his PhD from SFU in 1989. After a couple of years as a faculty member in Regina he came back to UVic, where he has been a faculty member since 1992. His interests mostly lie in the intersection of mathematics and computer science, and also include mathematics education, mathematics in sports, and combinatorial games.

**Speaker:** Dr. David Goluskin

**Title:** A simple mathematical model with very complicated consequences

**Abstract:** We will explore properties of a simple mathematical model called the logistic map. This model arises naturally when thinking about how the size of a population might change from one year to the next. Despite the simplicity of the equation, its consequences can be very complicated. By experimenting with these consequences, you will be introduced to the concept of “chaos”. I will demonstrate some computer code too.

**Bio:** David Goluskin is an applied math professor at UVic. His research is about nonlinear differential equations. He develops general methods for studying these kinds of equations, and he studies particular equations coming from scientific applications. The application on which he works the most is the behaviour of fluids (like air and water), which are governed by relatively simple equations but display extreme complexity. Before coming to UVic, David completed his undergraduate degree at the University of Colorado and his PhD in applied math at Columbia University, in New York, and then he was a postdoctoral researcher at the University of Michigan.

**Speaker:** Dr. Kieka Mynhardt

**Title:** The Hunting of the Snark

**Abstract:** “The Hunting of the Snark” is a poem by Lewis Carroll. A crew of ten on a sailboat try to hunt the Snark, a creature which may turn out to be a dangerous Boojum. The only crewmember to find the Snark vanishes, which means that the Snark was indeed a Boojum. Graph theorists also hunt Snarks, but our Snarks are not dangerous and, although it took a while to find them, we now know that there are infinitely many Snarks. A graph (or network) consists of vertices (think “dots” or “small discs”) connected by edges (think “lines”). We want to colour the edges of a graph in such a way that all the edges that meet at any given vertex have different colours, and we aim to use as few colours as possible. A Snark is a graph in which, among other things, exactly three edges meet at any vertex, but the edges cannot be coloured as described above using only three colours. In this talk, I will explain precisely what a Snark is, give examples of some of them, show how to make larger Snarks using smaller ones, and explain why Snarks are important to graph theorists.

**Bio:** Kieka Mynhardt is a professor of mathematics at UVic. Her research area is graph theory. She specializes in graph protection but is also interested in graph colourings. She was born in Cape Town, South Africa, obtained her PhD from the University of Johannesburg, and worked at the University of South Africa until joining UVic in 2002. Throughout her career she encouraged young women to study math and, especially, to pursue math graduate studies.

**Speaker:** Dr. Asmita Sodhi

**Title:** Pentomino Puzzlers

**Abstract:** A pentomino is a shape made by joining five equal squares side-by-side – think TETRIS, but with five squares instead of four. Together we’ll discover the different possible pentominoes, and explore some games and tiling puzzles that use these shapes.

**Bio:** Asmita 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:** Shannon Ogden

**Title: **Induction Deduction, What’s Your Function?

**Abstract: **Throughout these sessions, we have seen examples of inductive reasoning in various areas of mathematics. In this session, we will explore the principle of mathematical induction, and how it can be used to prove statements quantified over all integers greater than or equal to some given integer.

**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.