PMATH Prof Talk: Chatchai Noytaptim

November 26, 2024

3:00 PM–4:00 PM
DC 1350

Abstract: The amalgamation of dynamical systems and number theory has gained considerably interest in recent decades. This relatively young field of mathematics is known as arithmetic dynamics. In this talk, I will start by introducing basic complex dynamics of quadratic polynomials and studying simple iteration (i.e., polynomial composition). Then we will see the famous picture of the Mandelbrot set and many beautiful pictures of the filled Julia set. Additionally, I will discuss a research question that can be viewed from a perspective of number theory. No background in number theory and complex dynamics is required.

Over 9000

November 25, 2024

5:30 PM–7:30 PM
DC 1351

SASMS II

November 20, 2024

6:30 PM–9:00 PM
MC 4021

6:30 - 7:00 PM: Michael Alexander — Put a PINN in It

Abstract: Machine Learning has, in the past years, become tremendously useful for science. In particular, the flexibility and power of Neural Networks has found a home in many places, from
curve fitting to experimental control. However, ultimately we fear that our models don’t truly
understand the world and will eventually start spewing garbage. This is bad.

In this talk, I will give a brief introduction to Neural Networks, and then do a brief dive into
some of the methods scientists use to cope with this problem. Specifically, I want to cover Physics Informed Neural Networks (PINNs), a paradigm which seeks to complement the uncertainty of machine learning with the certainty of differential equations to put physicists’ minds at ease.

7:00 - 7:30 PM: Lily Mueller — I Know Where Your Air Is From (I Live In Your Air Condi- tioner)

Abstract: We describe the fundamentals of how the NOAA HYSPLIT model works and how to use it to compute air parcel trajectories.

7:30 - 8:00 PM: Tahini’s — Food

8:00 - 8:30 PM: Edmond Yu — How to Order the Complex Numbers

Abstract: It’s well known that the complex numbers can’t be ordered. Or, the issue is actually that there’s no ordering that satisfies the ordered field axioms. But what if we really wanted to order the complex numbers? Here we present a rather interesting way to “order” something and it gives us some insight to what “ordering” something really means, and it applies not to just ordering the complex numbers, but to some linear algebra as well.

8:30 - 9:00 PM: Kareem Alfarra — Algebraic Geometry: Intuition, Algebra, Combinatorics, and an Interesting Intersection Problem!

Abstract: Algebraic geometry is often considered a vast and seemingly mysterious field. We aim to uncover that mystery and give some basic intuition as to why we consider algebraic geometry. What is some basic intuition regarding the topic and its connections to algebra and combinatorics? How do we utilise the algebra, the combinatorics? How do they reveal information about the geometry?

Using the above, we explore an interesting intersection problem regarding an object in algebraic geometry called the Grassmannian, and how we make concrete the abstract ideas we explained earlier!

C&O Prof Talk: Stephen Melczer

November 19, 2024

5:00 PM–6:00 PM
MC 4040

Title: Adventures in Enumeration

Abstract: We make the argument that by combining pure mathematical tools with computational insights and applications from a vast array of disciplines, combinatorics is the perfect area to see all the wonders of math on display. Applications discussed include the analysis of classical algorithms, restricted permutations, models predicting the shape of biomembranes, queuing theory, random walks, ratchet models for gene expression, maximum likelihood degree in algebraic statistics, transcendence of zeta values, sampling algorithms for perfect matchings in bipartite graphs, and parallel synthesis for DNA storage.

C&O Prof Talk: Oliver Pechenik

November 11, 2024

5:00 PM–6:00 PM
MC 4042

Come for another long awaited Pechenik's incredible talk titled "Minuscule Doppelgangers"

SASMS I

November 7, 2024

6:30 PM–9:00 PM
MC 4021

6:30 - 7:00: Liam McQuay - An Introduction to Non-commutative Probability Theory

A random variable on a probability triple is often thought of as a “suitable” function which takes an element of the sample space into R or C. This allows us to take sums and products of random variables, giving the set of all random variables the structure of a commutative algebra. But can we can generalize this in a way where the random variables have a general (non-commutative) algebra structure? If so, how do we make sense of expectation, distribution, independence, and other related concepts?

We shall see that this point of view leads to a broad field known as non-commutative probability theory, and in this setting we need to reconsider how these notions are defined. The non-commutative analogue of independence here is known as free independence (though there are other types too!), and with it we get a corresponding analogue of central limit theorem by replacing “independence” with “free independence” (which we shall hopefully get to if time permits).

7:00 - 7:30: Easty Guo - A Fairly Cool Theorem That Would Fit in PMATH 351

In this talk, we will be going over a proof of Korovkin's theorem, a fairly obscure but very surprising theorem about continuous functions on a closed interval. We will also see how this theorem gives a quick proof of the Weierstrass approximation theorem from PMATH 351.

8:00 - 8:30: Henri Kennedy - Weird 17th (And 18th)-Century Nonsense That Works for Some Reason

We look at some of the heuristics and informal methods used in the 17th and 18th-century development of infinitesimal calculus and in 18th-century pre-rigourous analysis, using them to solve some simple problems. These include Leibniz's “Transcendental Law of Homogeneity”, Cauchy's “Generality of Algebra” (which he gave the name to but actually rejected in favour of the rigorous methods he helped develop), and Fermat's “Adequality”. Finally, we also cover Kepler and Leibniz' “Law of Continuity” and discuss its connection to the Compactness Theorem in Mathematical Logic.

8:30 - 9:00: Alex Pawelko - 2-Out-Of-3 Ain’t Bad

Here are three cool areas of geometry: the geometry of lengths and angles, complex geometry (the geometry of multiplication by i), and the geometry of conserved quantities (like conservation of energy or momentum from physics). Did you know that given any space with 2 of these geometries, you get the 3rd one for free? That's amazing!!!!

In my talk, I'll explain the basic ideas behind these geometries and explain why 2-out-of-3 is true (I will just be using linear algebra, no differential geometry required).

AMATH Prof Talk: Francis Poulin

October 22, 2024

5:00 PM–6:00 PM
DWE 1515

Chaos and Power!

Edward (Ed) Lorentz is often called the father of Chaos. He was a professor at MIT, not in Mathematics but in Meteorology. In 1963 he published a paper entitled “Deterministic nonperiodic flow” that introduced a Strange Attractor and the idea of the Butterfly Effect, what we now strongly associate with Chaos. Even though Chaos is well known in popular science, the scientific community cannot seem to agree on a precise definition of “What is Chaos”? But one characteristic that is always present in each definition is the idea that Chaos is unpredictable, which makes weather prediction such a hard problem.

This talk will consist of two parts. In the first I will give an introduction to the famous Lorentz model and how it was derived in an attempt to idealize Atmospheric Convection. Ed discovered that this model, as trivial as it seems in comparison to the real atmosphere, is essentially unpredictable, and hence chaotic. In the second I use Fourier Analysis to determine the Power Spectrum of a time-series and show how this introduced a natural definition for chaos. Therefore, through power we can better understand Chaos.

AMATH Prof Talk: Brian Ingalls

October 8, 2024

5:00 PM–6:00 PM
DWE 3818

Join us for food and to learn about biological modelling using maths !!!

Abstract: Molecular biology offers a powerful substrate for impacting health, agriculture, manufacturing, and environmental remediation. Mathematical modelling tools are frequently used in model-based design of such developments. We will begin by outlining how the behavior of such molecular systems can be described by systems of nonlinear differential equations. We then describe an ongoing research project on modelling of a novel bacteria-mediated cancer therapy.

F24 Disorg

September 10, 2024

5:00 PM–7:00 PM
MC 5479