Three CUMC 2019 Talks

Hi everyone! Our next event will be talks from the 2019 Canadian Undergraduate Mathematics Conference (CUMC) by three students, Isabel Beach, Curtis Michael and Nikki Sigurdson. It will be Friday, October 25th, 2019 at 6:10pm, in BA 6183.
Pizza and pop will be provided!

The talks:

The Beauty of the Hyperbolic Plane, by Isabel Beach

An Introduction to Mapping Class Groups and the Nielsen-Thurston Classification of Mapping Classes, by Curtis Grant

Finite Model Theory and First Order Definability, by Nikki Sigurdson

Hoodies available for pickup

Math Union Hoodies are available for pickup tomorrow (Monday, April 8th) from 1:30-4:30 pm in the math undergrad lounge. More times for pick up will be announced tomorrow night.

You must bring your t-card in order to pick up your hoodie. See you tomorrow!

Professor Candidate Talk: Cindy Blois

Cindy Blois, Thurs Jan 31, 4:30-6:00, BA6180

Title: Path-Ordered Exponentials

Abstract: In this talk, we will look at calculus through a new lens as we approach the definition of the path-ordered exponential. We will see that the path-ordered exponential arises naturally in the solution of first-order linear systems of ODEs (with variable coefficients) and is also a stepping stone toward path integrals in quantum physics.

99% of this talk will be accessible to undergraduates that have some experience with introductory analysis and linear algebra. However, 1% will be accessible to no one, because it will be utter nonsense.

Professor Candidate Talk: Yu-Wen Hsu

Yu-Wen Hsu, Wed Jan 30, 5:00-6:30, BA6180

Title: The Power of Geometric Evolution Flow

Abstract: What numerical characteristics do geometric shapes have? You will probably think of the length of a curve, or the volume of a 3-dimensional shape, or an angle between two directions in space. In this talk we will discuss a characteristic of curves called curvature, which measures the sharpness of a turn while moving along a path.

It turns out that this characteristic controls the process of curve evolution, called the CSF, “curve shortening flow”. We will talk about some important work that was done in the 80s on curves in R^2 and see how the CSF can reshape a curve.

Professor Candidate Talk: Steve Bennoun

Steve Bennoun, Thurs Jan 24, 4:30-6:00 pm, BA6180. Pizza.

Title: A Peek into Category Theory

Abstract: Have you ever heard about categories? What are they? What are they useful for?

We will start the following question: take two groups G and H and look at the set of homomorphisms between them. Does this set have a group structure? To answer this question, we will introduce some basic notions of category theory. We will reformulate our question in categorical terms and then see how categories help us solve it. Along the way, we’ll define what categories and functors are and look at examples. We’ll actually see that many mathematical objects we know are categories.

MU Hoodies

MU Hoodies are here!!

Hoodies are $25 each. Payment must be made in CASH only (exact change preferred). To order, first fill out the online order form, and then bring the $$ to the Bahen 6th floor Undergrad lounge over the next two weeks. A list of times of when you can pay for your hoodie will be posted over the weekend.

ORDER FORM:

https://docs.google.com/forms/d/e/1FAIpQLSePAOawO8ORn6e2eTOVfLgR_VRdJcXhDZyvnABA8tYICZkUhA/viewform?usp=sf_link

Thank you to Lola Bradford and Arthur Qiu for helping with the design!!

If you have any questions/concerns, please email me at rebecca.moranis@mail.utoronto.ca

Professor Candidate Talk: Lindsey Shorser

Lindsey Shorser, Thurs Jan 17, 12:30-2:00 pm, BA6180. Pizza.

Title: Categories: What, Why, and How – An Introduction

Abstract: Category theory can be seen as a language that allows common features to be abstracted out of mathematical objects such as sets, vector spaces, groups, topological spaces, etc. In this talk, we will look at the flavour of categorical thinking with same basic definitions and examples. Then we will discuss commutative diagrams and why homological algebra and category theory are inextricably intertwined.

Professor Candidate Talk: Fabian Parsch

Fabian Parsch, Wed Jan 16, 5:10 – 6:00, BA6183. Pizza begins at 4:30.

Title: Fantastic Nets and Where to Find Them

Abstract
Take a sheet of paper and draw three points in the plane. Now connect them with curves, but try to make the total length of all curves as short as possible. After some experimentation, you will probably arrive at a good guess of a best solution. But how do you know this is in fact a best solution? How do you know it is the only best solution? How do you even know there is a best solution? What if you have to connect four points instead? Five? n?
These are the kind of questions that are answered by the concept of geodesic nets.
The best thing about geodesic nets is that they are very easy to define, as we will see in the talk. The worst thing about geodesic nets is that not much is known about their behaviour, even in the simplest case: connecting points on the flat plane. If we look at other surfaces (like the sphere or a torus), things only get worse.
In this talk we will define what geodesic nets are, talk about some known results and discover some “animals“ in the zoo of nets together. Time permitting, we will also have a look where geodesic nets appear in architecture and material science.
The talk has only minimal prerequisites (see below). As long as you bring along an intuitive understanding of geometry, you are ready for take-off!
Prerequisites
Euclidean Geometry, Linear Algebra
Helpful (but not necessary!)
Elementary Surfaces (Sphere, Torus), Geodesics, Curvature
Also Helpful
You have been inside the Roger‘s Centre while the roof was closed.
Bringing your Laptop for some experiments is encouraged!