2020
| Date | Time | Location | Speaker | Title |
|---|---|---|---|---|
| Jan 21 | 5pm | LOV 201 | Francesca Bernardi | A First Approach to the Advection-Diffusion Equation |
| Jan 28 | 5pm | LOV 201 | Samuel Glickman | An Undergraduate Introduction to KPZ Universality |
Francesca Bernardi
A First Approach to the Advection-Diffusion Equation
Abstract: The advection-diffusion equation is one of the fundamental equations of fluid dynamics and describes the spreading of a dissolved species in slow fluid flow within a pipe. In this talk I will discuss how an applied mathematician would first approach this equation: we will start by non-dimensionalizing the equation and defining the Péclet number, a very useful non-dimensional parameter in this context. Then, we will apply scaling arguments to simplify the equation and attempt to solve the problem for a couple of well-known cases.
Samuel Glickman
An Undergraduate Introduction to KPZ Universality
Abstract: Over the past 35 years, mathematicians and physicists have been investigating a new probabilistic law known as the Tracy-Widom distribution that arises from random systems with interacting components. Asymptotic analysis of these systems has resulted in a new universality class of complex random systems called the Kardar-Parisi-Zhang (KPZ) universality class. In this talk, I will discuss some of the foundational elements of probability theory and their connection to universality classes of random systems. We will then examine the KPZ universality class, the current state of KPZ universality research, and my experiences as an undergraduate student working to understand this topic.
2019
| Date | Time | Location | Speaker | Title |
|---|---|---|---|---|
| Sep 12 | 5pm | LOV 201 | Alex Vlasiuk | How much does this matchbox know? |
| Sep 17 | 5pm | LOV 201 | Arash Fahim | Probabilistic implications of a simple formula: sin(2x)=2sin(x)cos(x) |
| Sep 24 | 5pm | LOV 201 | Arash Fahim | How far does a random walk take us? |
| Oct 22 | 5pm | LOV 201 | Matthew Russo | Solitons: Why isn't that wave breaking? |
| Nov 12 | 5pm | LOV 201 | Francesca Bernardi | Scaling your way out of trouble: How to simplify your mathematical life with dimensional analysis |
| Nov 21 | 5pm | LOV 201 | Ben Prather | Hypercubic self-tilings |
Alex Vlasiuk
How much does this matchbox know?
Abstract: What is information and how is it measured? Before Shannon published his famous paper in 1948, we could not really tell how much we knew. Neither could we compute how much knowledge was concealed in the world around us (spoiler: a lot). In this talk we discuss how to quantify information contained in a system or produced by a source, and how it can help in making communication more reliable.
Slides: [pdf]
Arash Fahim
Probabilistic implications of a simple formula: sin(2x) = 2sin(x)cos(x)
Abstract: We consider the famous Vieta formula derived from sin(2x) = 2sin(x)cos(x) and relate it to probabilities of flipping a coin in independent sequential trials.
Slides: [pdf]
Arash Fahim
How far does a random walk take us?
Abstract: Walking around guided by a coin toss, we count how many times we come back to the starting point, on a line, in the plane, and in the space.
Slides: [pdf]
Matthew Russo
Solitons: Why isn't that wave breaking?
Abstract: In this talk I will give a brief introduction to special nonlinear waves of permanent form, called solitons. Roughly speaking, solitons represent a balance between linear and nonlinear effects which result in a wave propagating through a medium without change of form. We'll delve into a brief history of solitons, the physical and mathematical mechanisms for their creation, the variety of forms they come in, and the contexts in which one may find them.
Slides: [pdf]
Francesca Bernardi
Scaling your way out of trouble: How to simplify your mathematical life with dimensional analysis
Abstract: When beginning a new research project most applied mathematicians start by non-dimensionalizing the model that describes their system of interest. The process of non-dimensionalizing consists in taking the dimensional quantities (with units!) involved in the model and making them dimensionless. Although this procedure is rarely taught in math classes, it is fundamental to applied math research because it has several surprising advantages. In this talk I will give an introduction to non-dimensionalization procedures. I will discuss how scaling equations appropriately can simplify models and solutions. Finally, I will show how these processes apply to the advection-diffusion equation.
Slides: [pdf]
Ben Prather
Hypercubic self-tilings
Abstract: Number theory tells us that a hypercube can be tiled by any sufficiently large number of hypercubes. Finding the largest number n for which the tiling is still impossible is a much harder problem. In dimensions d=2 and d=3, n is known to be 5 and 47 respectively. For d=4 we have an upper bound of n≤733.