Micheal Pawliuk: A History of Functions

We’ll have a Math Union talk next week on Tuesday, March 10 at 6:10pm in BA 6183. Prof. Micheal Pawliuk will be speaking about the history of functions! As always, there will be food.

Title: A History of Functions

Abstract: What is a function? Our current definition is surprisingly recent, and it figuring it out was a result of important questions in mathematics and physics. Updating our definition resulted in having to “redo” a bunch of seemingly solved mathematics.

We’ll trace the history of functions from the mid 1800s forward to the birth of topology.

Kasun Fernando: Statistical Properties of Dynamical Systems

 

There will be a Math Union lecture on Wednesday, March 4, at 5:10pm in BA024. Kasun Fernando will be speaking about the statistical properties of dynamical systems. Food will be served!

 

Title: Statistical Properties of Dynamical Systems

 

Abstract: Since the work of Boltzmann in statistical mechanics, physicists and mathematicians alike were interested in looking at deterministic chaotic systems with a probabilistic eye. Later, with the mathematical foundations laid out by Birkhoff, Kolmogorov and von Neumann, the systematic study of statistical properties of dynamical systems aka Ergodic Theory started to flourish. My talk will be a brief introduction to this probabilistic approach to making sense of chaotic phenomena.

Christian Ketterer: Synthetic curvature bounds – A friendly introduction

Hi everyone! We will be having our first talk of the semester on Tuesday, January 28th, 2019 at 4:10pm. A post doc Christian Ketterer will be speaking.

Details of the room will be announced shortly!

Title: Synthetic curvature bounds – A friendly introduction

Abstract: In this talk I will explain the concepts of synthetic sectional curvature bounds and synthetic lower Ricci bounds and the ideas behind them. Synthetic lower Ricci bounds originated in the last 20 years from the encounter of several mathematical fields, including Riemannian Geometry, Optimal Transport and Information Theory. I will briefly describe these fields and show how they mixed.

Graduate Applications Workshop – this Thursday

Hi everyone! Just a reminder that this Thursday, Jan 9, there will be a graduate applications workshop at 4pm in BA6183. For those of you who are applying to graduate schools now or are interested in applying in the future, this is a great opportunity to hear about the application process, what can be expected, and to ask specific questions to faculty and graduate students. Please fill out the (short!) RSVP form below if you are interested in attending – there is a space to ask specific questions in the form in advance!

The form: https://forms.gle/jYh46M8zBK2xWnkbA?fbclid=IwAR3Sd4aUNvYqVglxi9jUGQvr8vXVLvM3GLNO4fIFKq-Mb0ZI-Avf4fVakKc

Happy new year!

Graduate Application Workshop

Hi everyone! For those of you applying to graduate schools with deadlines in January, as well as those who are perhaps thinking of applying to graduate schools in the future, we will be holding a graduate applications workshop on January 9 at 4pm in BA6183. There will be a faculty panel, as well as a graduate student panel, and an opportunity to ask questions about the application process and the like.

If you are interested in attending, please fill out the Google form below and include any questions you have for the panel.

Happy holidays!

https://forms.gle/jYh46M8zBK2xWnkbA

Justin Martel: Energy vs. Mass Transport

Join us for our last talk before the new year, given by Justin Martel, a former graduate student at U of T. The talk will be Thursday, December 12th at 5:10pm in BA6180. Pizza will be served in the Graduate Lounge at 4:40pm.

Abstract: Is the distance from Toronto to Moscow today the same as the distance 2000 years ago? To the mathematician, ”Surely not!” when the distance is reckoned at 7500 kilometers ac- cording to the model globe in his office. But ”Distance” as- sumes entirely different dimensions when measured in terms of Energy-variables. A distance changes when the actual transit is taken into account. And how is it possible for the Hominid, capable of sustaining only an average of 75 Watts throughout an eight hour day, to transverse such great dis- tance?

This talk will describe, in simple terms, the principles of Optimal Transportation. We will focus on elementary physical models, energy, and Least Action Principles.

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

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.