Graduate Student Advisory Committee (GSAC) Colloquium Schedule:

Welcome back.

This is an organizational meeting in which we'll discuss plans for upcoming events and colloquia.

Queuing systems in tandem with discontinuous service times

Imagine the following bureaucratic nightmare: You are a entering a bank and upon entering you join the queue in front of the first and only available server. Naturally you await your turn, and after your job is done the server tells you you need to go to a second server and join the queue there. He tells that to all people though, so naturally there's a queue waiting for you there. Then the second server sends everyone to a third and so on and so on... Fun, right?

Two natural questions is the expectation of the exit time from the system and whether a bunch of slow servers create traffic in the system (i.e. queues grow). The above somewhat unrealistic example is a version of what's called in interacting particle systems a " totally asymmetric simple exclusion process (TASEP)." During the talk we will talk about TASEP in the disguise of a queuing system and as a disease spreading model. if time permitss we'll spend a little time explaining a connection with certain PDE's with discontinuous coefficients. All unknown words in the abstract and title will be explained during the talk.

5 reasons to care about Riemann's zeta function

The zeta function has been the object of intense study for nearly 300 years by mathematicians from a variety of backgrounds. It made an appearance in Hilbert's list of problems in 1900 and made the cut again in the Millennium problems. So, why all the hubbub? The short answer is that the zeta connection provides a connection between analysis and number theory that is fascinating and surprising, and that dramatically influenced the course of related research for the last 150 years. The purpose of this talk is to highlight just a few of the interesting aspects of the zeta function and to discuss its role in modern mathematics.

Lamps and groups and geometry, OH-MY

This colloquium will investigate the Lamplighter group. An interesting heuristic will be developed to better understand this rather exotic group. The study will be from a geometric point of view. Several surprising results about the geometry will of Lamplighters will leave the audience saying "OH-MY."

DVRs that don't record videos

The field of p-adic numbers is the completion of the rational numbers with respect to the p-adic absolute value. The corresponding topology on the p-adic integers is consistent with the ring's natural topology as a local ring. In this talk, I'll introduce the concepts of discrete valuation rings and describe the algebraic structure of such objects to make sense of the above statements. This talk will be geared towards a general math audience, with a few asides for those more comfortable with these objects.

Colloquium cancelled

There will be no talk this week.

Geophysical Methods Applied to Sea Ice

In this talk I will develop a common electromagnetic geophysical model used in prospecting to see what is underneath the ground below your feet. It supposes that the earth is made of horizontally stratified layers of rock each with a different resistivity. By injecting current into the ground and measuring the results one can determine what the structure of the rock layers is below. I will show how this method can be applied to sea ice to characterize its structure as well as validate other models for the resistivity of sea ice.

Fall break!

There will be no colloquium this week.

An overview of the mathematics behind CAT scans

Can one determine a function from knowledge of its line integrals? Ultimately, this is a question related to integral geometry which has had profound applications in medicine. Although the problem was essentially solved by Johann Radon in 1917, it wasn't until 1979 that Allan Cormack and Sir Godfrey Hounsfield received the Nobel Prize in Medicine for their work on X-ray tomography. In this talk, I will introduce some of the mathematics involved in CAT (in particular the Radon transform) and present some (basic) simulations illustrating how a CAT scanner works.

A Molecular Motor Inspired Path Dependent Markov Problem

A type of model gaining traction in the study of molecular motors is a chemomechanical state model. This type of model breaks a single ATP step cycle of a motor into its chemical and mechanical components. The resulting state model graph can then easily be represented as a Markov Chain. The transition times and transition distances of this Markov chain, however, are all different. How can we then extract values like Expected Run time or Expected Run Difference from this Markov process when different paths to the same state take different times and distances?

A few of my favourite things.

... these are a few of my favourite things. I will talk about some of the things I've found in mathematics that inspire and motivate me. Also, I will spell favourite with a 'u' because that is one of my favourite things to do.

Colloquium cancelled

There will be no talk this week.

Introduction to Outer Space

The study of automorphism groups of free groups is old but the geometric approach to these groups is relatively new. Outer space was introduced in 1986 by Culler and Vogtmann as a tool for studying the group of outer automorphisms of a free group F_n. Basically outer space is the set of points corresponding to finite graphs with fundamental group isomorphic to F_n. In this talk I will carefully define this space and I will present some of its features.

Thanksgiving week!

There will be no colloquium this week.

The Geometry of Origami

This talk will focus on the underlying geometry of origami, starting from the seven Huzita-Hatori axioms. We will explore some interesting and surprising results about traditional origami, including the facts that one can trisect an angle and double a cube. We will discuss rigid and modular origami and their applications, and conclude by working together to construct polyhedra from smaller modules.

Interesting Theorems

The topic of this talk will cover the proofs of some simple, yet important, theorems that one should encounter as an undergraduate. Background needed to understand this talk includes function notation and knowing how to add and multiply numbers.