Greenslopes Seminar

[Department of Mathematics]
Thursdays 11AM Weber 202
Co-Organizers: Eric Miles and Bethany Springer

Schedule:

For the seminar attendance sheet, click here.
Abstracts appear below.

Date Speaker Title Advisor
Jan. 31 Tegan Emerson More Cancery Stuff (and a discussion about a paper about sort of relevant stuff) Michael Kirby
Feb. 7 Justin Hughes The Group Action on the Chain Complex given by a Cayley Graph. Chris Peterson and Alexander Hulpke
Feb. 14 Brent Davis Real Algebraic Geometry Dan Bates and Chris Peterson
Feb. 21 Bethany Springer Nearly Continuous Dynamics, a Story Book Andres del Junco and Patrick Shipman
Feb. 28 Mary Worthley "Why are my Calculus students so bad?" Gene Gloeckner and Paul Kennedy
Mar. 7 Christopher Strickland Zombie Attack! Modeling the Dynamics of a Zombie Apocalypse Patrick Shipman
Mar. 14 CANCELLED!!! Please attend Magnus Lecture
Mar. 21 Spring Break
Mar. 28 Douglas Ortego The Wonderful Wizardry of Winding Numbers Renzo Cavalieri
Apr. 4 Melissa Swager Hi Ho Cheerio and Lipid Rafts! Young Cheng Zhou
Apr. 11 Cory Previte Reduced Homology of the D-Neighborhood Complex on Simple Graphs Chris Peterson and Alexander Hulpke
Apr. 18 Drew Schwickerath Michael Kirby and Chris Peterson
Apr. 25 Tim Marrinan 'Capture the flag: classifying multi-labeled data on a manifold with positive curvature.' Michael Kirby
May 2 Anne Ho Title Rachel Pries
May 9 Lori and Bethany The Stuff we Didn't Know--Tales of grad school and job hunting not enough (or too many)
May 16 Finals Week

Abstracts:


Jan. 31 - - Tegan Emerson

I will be discussing the attached paper as it pertains to my research. Additionally, I will discuss some of the updates in my research and the general topic of publications and what options arise when a paper is published on a very similar topic.

Feb. 7 - - Justin Hughes

Given a Cayley graph $G=(E,V)$ and a distance set $D=\set{\set{a_1,a_2,...,a_n}|a_i\in\Z^{+}}$, we can construct a simplicial complex. This simplicial complex leads to a chain complex in the usual way. Since the Cayley graph is constructed from a group there is a natural group action on the graph and so induces an action on the chain complex. We will discuss this action and see that the irreducible representations corresponding to this action are predictable by a few calculations on the generators which are used to create the Cayley graph.

Feb. 14 - - Brent Davis

I will give a crash course on some ideas from real algebraic geometry. I'll focus on quantifier elimination, Descartes's rule of signs, Motzkin polynomial, Sturm sequences, and cylindrical algebraic decomposition (as time allows).

Feb. 21 - - Bethany Spriniger

Nearly continuous dynamics blends together ergodic theory and dynamical systems by asking that properties hold modulo sets both topologically and measure-theoretically small. And, if half of the words in that sentence did not make sense, do not be afraid. This talk, actually my job-talk for on-campus interviews, is designed to be friendly and approachable, and includes a plethora of pictures and examples along the way. So, come see pictures of odometers, irrational rotations, cuttings and stackings, and much, much more!!



Feb. 28 -- Mary Worthley

Mary's Abstract



Mar. 7 -- Christopher Strickland

In this talk, I present several ODE models for zombie invasion and analyze them to determine the fate of mankind. Largely based off the 2009 paper "When Zombies Attack!: Mathematical Modelling of an Outbreak of Zombie Infection," this talk will serve as an introduction to epidemiological modeling and review basic dynamical systems analysis for nonlinear systems. It will be particularly applicable to graduate students teaching Math 255 or Math 340, since the simplest zombie model is easily analyzed by hand and can serve as an in-class example for Jacobian eigenvalue/eigenvector methods. There will also be plenty of zombie pictures.



Mar. 28 -- Douglas Ortego

Winding numbers are in my mind subtle versions of classes in the fundamental group of subspaces of the real plane. I will spend a few minutes defining and giving a handful of their properties before going on to show how they can be used to prove a smorgasbord theorems including but not limited to the fundamental theorem of algebra, the Borsuk-Ulam theorem, invariance of dimension, and the famous ham sandwich theorem. I may not have time to go through all of the theorems listed or I may have time to go through others unlisted. Only time will tell. Thanks for reading this!



Apr. 4 -- Melissa Swager

Does eating Cheerios really lower your cholesterol and can it save your life? An introduction to the life of a lipid raft and recent studies in the area. Come learn how math could help save the life of a human!



Apr. 11 -- Cory Previte

Using a loose analogy of being a construction worker, I will describe my ``toolbox'' and how I use these tools to build the objects I am studying. In particular, how I am using ideas from Combinatorics and Algebraic Topology to study the homology of a special kind of simplicial complex formed from a set of distances in a combinatorial graph. From here, we will make statements about the homology for certain graphs. Don't be daunted by the title; every word will be defined and I've included pictures (relevant and irrelevant) to make the talk enjoyable for everyone.

Apr. 25 -- Tim Marrinan

The Carnegie Mellon "Pose, Illumination, and Expression database" is a set of images of people under different lighting conditions. It is used as a baseline for many computer science applications. One notable result in mathematics/cs that can be illustrated with this data set is that the illumination space of an object forms a convex cone in R^n. I will use this data set to talk about representing data as linear subspaces, results on classification from the literature, limitations of those results, and why treating collections of images with multiple semantically meaningful labels as a flag may improve classification.



May 2 -- Anne Ho

Quick response (QR) codes are printed on ads, package labels, business cards, and more. You can scan them with a smartphone and get a URL or other information. In this talk, I will discuss standards and versions of QR codes. Then, I will work through an example to encode a simple phrase. Finally, I will talk about error-correction and how this tangentially relates to my research.



May 9 -- Bethany Springer and Lori Ziegelmeier

Perhaps you occasionally feel in the dark about the goings on in graduate school, the true meaning of a PhD, and what awaits you as you enter your final years of school and prepare to graduate. In this talk, Lori and Bethany will reveal to you what they wished had been revealed to them as they bumped along in the dark. They will mostly share advice and stories on the job application process. While this talk may shock or terrify you, or even make you laugh, hopefully, you will walk away feeling either more prepared or knowing how to prepare for the tough times to come.





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