The Department of Mathematics is hosting a regular seminar series. The goal of the seminar is to bring together students and faculty members to discuss interesting mathematics! Each speaker will present a topic of their choice with the intent that the talk will be accessible to undergraduate students. Typically a talk will be around 50 minutes, with 10 minutes reserved for questions. Talks may be a survey about a particular area of math, a tutorial about a specific topic, or an introduction to a research area with discussion about recent results. Everyone is welcome to attend!
If you are interested in speaking at the seminar, please contact one of the organizers, Cobus Swarts (jacobus.swarts (at) viu (dot) ca) and Melissa Huggan (melissa.huggan (at) viu (dot) ca).
Dates, times, and locations for upcoming seminars are below.
Upcoming Seminars
September 27 at 4:00pm (Building 210, Room 270)
- Speaker: Matthew Debolt
- Title: The Abstract Nonsense of Category Theory
- Abstract: What can be said to exist?
In the 19th and 20th centuries, significant mathematical advances were made by taking interest in things and their properties. Algebraic topologists Eilenberg and Mac Lane shifted their attention to the relationships between things in the 1940s, and the result was category theory. Owing to its extensive use of diagrammatic argument, it is endearingly referred to by practitioners as “abstract nonsense.”
We will tour the main ideas of category theory and consider their applications. A category is a thing which collects things and their relationships—the category’s objects and morphisms. It follows naturally to consider morphisms between categories, known as functors. Next, we consider morphisms between functors; these are natural transformations. Using this language, we can characterize objects without reference to their internal properties. Instead, we find universal properties of how certain objects relate to different objects. Time permitting, we may discuss the Yoneda Lemma and the dimension of categories.
- October 4 at 4:00pm (Building 210, Room 270)
- Speaker: Dr. Dave Smith (Yale-NUS College, Singapore)
- Title: Linear algebra in initial boundary value problems
- Abstract: Initial boundary value problems and partial differential equations model many phenomena in physics, from conduction of heat to waves on the ocean, but present challenging mathematical problems. We will show how they can often be encoded as eigenvalue problems which are then much easier to solve. We will explore how derivatives can be seen as linear operators in infinite dimensional vector spaces, how they can be diagonalized, and how all this relates to solving initial boundary value problems. This will lead us to some recent research in solving initial boundary value problems with applications to water waves and diagonalizing differential operators.
October 25 at 4:00pm (Building 210, Room 270)
- Speaker: Dr. Heather Wiebe
- Title: (To be determined)
- Abstract: (To be determined)
- November 29 at 4:00pm (Building 210, Room 270)
Past Seminars
- April 14, 2023 at 3:30pm (Building 460, Room 324)
- Speaker: Dr. Gara Pruesse
- Title: Partially Ordered Sets and their hard, easy, and approximate algorithmic problems
- Abstract: We are frequently called upon to compare objects according to some metric, with one found to be greater and one lesser. Comparisons of the elements of a set result is a list of the elements in sorted order, each element less than the next, like the numbers 1; 2; 3; etc. Or so you would think. Some sets of objects, such as tennis players, may comprise a partial order: perhaps it is quite clear that Novak is a better player than Gara, but maybe Gara and Bette are “incomparable” in that one is not clearly better than the other. Partial orders arise naturally in many areas, in knowledge representation, preference rankings, operations research, and in scheduling, such as task scheduling for computer processors. There are journals dedicated just to partial order research, and other journals that publish only articles on scheduling.
This talk introduces partial orders and some of the interesting problems that arise from them. Some of the optimization problems on partial orders are computationally “hard” (NP-hard), but are nevertheless so useful that researchers focus on finding approximate solutions. The jump number problem is such a problem. Gara will present a classic result on jump number, with a new, elegant proof, as well as some other recent results that she will be presenting at the upcoming SIAM Conference on Applied and Computational Discrete Algorithms (ACDA ’23).
- March 24, 2023 at 3:30pm (Building 460, Room 324)
- Speaker: Dr. Alex Fok
- Title: Fun with spheres
- Abstract: Among all closed and bounded surfaces, spheres are the simplest, yet the most symmetrical and occur most frequently in the nature. Since the time of Archimedes, they have been objects of great interest in mathematics. In this talk, we will take a stroll through some fascinating properties of spheres and use them as toy models to get a taste of some far-reaching results in topology, an area of mathematics dubbed the rubber-sheet geometry.
March 17, 2023 at 3:30pm (Building 460, Room 324)
- Speaker: Dr. Melissa Huggan
- Title: Pursuit-Evasion Games: An Introduction
- Abstract: Pursuit-evasion games have been vastly studied over several decades by dozens of researchers worldwide. A central focus of this research has been on the game of Cops and Robbers. Player 1 controls a set of k cops, while Player 2 controls a robber. Player 1 chooses k (or fewer) vertices of a graph for the cops to occupy, then Player 2 chooses a different vertex for the robber to occupy. Players then alternate turns moving along edges of the graph. The goal of the cop player is to capture the robber by occupying the same vertex. The goal of the robber is to avoid capture indefinitely. This talk will take participants on a journey through key results from the literature of Cops and Robbers. We will conclude with a discussion of current research directions within the area of pursuit-evasion games.
- February 17, 2023 at 3:30pm (Building 460, Room 324)
- Speaker: Dr. Cobus Swarts
- Title: The Complexity of (Di)graph Homomorphisms
- Abstract: In this talk we will be discussing the computational complexity of (di)graph homomorphisms. This refers to the ease/difficulty with which this problem can be solved on a computer. The talk will begin by discussing what graphs are and what it means to colour a graph. At this point we will discuss the computational complexity of graph colouring. We then show that graph colouring is a special case of graph homomorphisms and that there is really more to the colouring problem. We will then introduce graph homomorphisms and talk about their computational complexity. If there is time left, we will discuss digraph homomorphisms and their computational complexity.