# CMU Graduate Student Seminar

## Fall 2016

### Organizer

If you would like to give a talk, please email me.

### Meeting Times

Tuesday, 4:00–4:50pm, in Pearce 227.

### Schedule

 Date Speaker Title (click Title for Abstract or scroll down) 8/30/2016 Callout (CMU Mathematics) A Message to All Gradaute Students 9/6/2016 Patrick Davis (Central Michigan University) A Practical Introduction to LaTeX -- Part I 9/13/2016 Patrick Davis (Central Michigan University) A Practical Introduction to LaTeX -- Part II ** 9/20/2016 No Seminar No Seminar 9/27/2016 Motohico Mulase (UC Davis) Department Colloquium 10/4/2016 Ayush Khaitan (Central Michigan University) Tropical Geometry -- An Introduction 10/11/2016 3:45 -- 5 pm Film Lecture -- Featuring Andrew Gleason (Harvard University) NIM and Other Oriented Graph Games ** -- link 10/18/2016 Carl Lee (Central Michigan University) Kelly Twigg (Central Michigan University) Non-teaching Industrial Internship -- Ideas, Applying, and Experiencing 10/25/2016 No Seminar No Seminar 11/1/2016 Ayush Khaitan (Central Michigan University) Category Theory 11/8/2016 Patrick Davis (Central Michigan University) Lessons from SMS: Infectious Disease Modeling 11/15/2016 Ana Dias (Central Michigan University) Combinatorial Game Theory 11/22/2016 Tim Rey (Advanced Analytics Stillcase, Inc.) An Overview of Advanced Analytics in Modern Industry 11/29/2016 205 Research Lab Tibor Marcinek (Central Michigan University) Getting to Know GeoGebra (Better) 12/6/2016 Matthew Moore (Central Michigan University) A Mathematical Model of Communication Between Cells to Determine the Tip/Stalk Fate

### Abstracts

Speaker: Patrick Davis (September 6 & 13)
Title: A Practical Introduction to LaTeX
Abstract: In 1978, Donald Knuth released the typesetting system TeX to produce consistent high-quality documents; and since then, a whole family of tools have been built on the TeX system. Today, the most widely used format is LaTeX, which was originally designed by Leslie Lamport in the early 1980s. LaTeX is free and may be used on all the major platforms (Mac, Windows, Linux, and online). Its ability to produce technical and scientific documentation with beautifully typeset mathematics has made it the standard in many academic fields. This seminar will run for two days:
Sept 6 : We will guide audience members through the installation process, and then demonstrate how to typeset a simple document in LaTeX.
Sept 13 : We will demonstrate how to do some more advanced typesetting, and tailor the demonstration to answer any specific questions raised by audience members.
Audience members are encouraged to bring their laptops to the seminar so that they can follow along.
Extra Information: See Demo (a pdf file) (the tex file for Demo) and recall what we discussed during the seminar.
AMS Graduate Student Chapter at CMU also provides excellent sources on LaTeX

Speaker: Motohico Mulase (September 27)
Title: Department Colloquium
Abstract: Click here for Title and Abstract

Speaker: Ayush Khaitan (October 4)
Title: Tropical Geometry -- An Introduction
Abstract: Tropical Geometry -- yes. It is as cool as it sounds. Polynomials branch out like trees. Analysis becomes combinatorics. And unlike the way that a lot of sufficiently advanced Mathematics is perceived, this has some real world applications too! It was used by the economist Paul Klempener to design auctions during the financial crisis. It also has applications to optimization, transportation, and so on.
And yes. It is called Tropica because it comes from a warmer part of the world. It was named in honor of the Brazilian mathematician Imre Simon, who wrote on the field. Come discover what wonders such an esoteric part of Math may contain.

Speaker: Andrew Gleason starring in the film lecture (October 11)
Title: NIM and Other Oriented Graph Games (published 1966)
Abstract:
We will be watching a film lecture published in 1966 featuring Professor Andrew Gleason of Harvard University on the above title. Notices of the AMS called Gleason "one of the quiet giants of twentieth-century mathematics". He made tremendous contributions to the society via his mathematical research and the innovative teaching styles.
The topic of Game Theory was suggested by a current graduate student.
Roughly speaking, Game Theory studies mathematical models on winning strategies. The theory has many applications to Economics, Biology, and Psychology, just to name a few.
This film lecture gives an introduction to the basic ideas growing out of the NIM game and their mathematical models. Not sidetracked by the subject's applications to other disciplines, the lecture focused mainly on the interesting mathematical part that comes into the studies of the subject.
*Film run time: approximately 65 minutes.
** Here is the link to the film we watched.

Speaker: Carl Lee and Kelly Dwigg (October 18)
Title: Non-teaching Industrial Internship -- Ideas, Applying, and Experiencing
Abstract:
Dr. Carl Lee will give an informative presentation about the idea of the non-teaching industrial internship, and the procedure about how one will apply the internship of this track.
Kelly Twigg did an internship this past summer and will share with the audience her experience.
A Q&A section will follow Dr. Lee and Kelly's presentations.

Speaker: Ayush Khaitan (November 1)
Title: Category Theory
Abstract: Category Theory is an alternative to set theory as a foundation for Mathematics. It is a universal framework constructed in order to study the relations between various mathematical objects that do not manifest themselves easily. Hence, it is an incredibly powerful tool that mathematicians use to see the "bigger picture".
However, Category Theory is also notoriously difficult to learn and understand at first. The dearth of readable introductions doesn't make it any easier. The aim of my talk will be to introduce some elementary tools in Category Theory, so that one may be encouraged to pursue the topic further.

Speaker: Patrick Davis (November 8)
Title: Lessons from SMS: Infectious Disease Modeling
Abstract: S\'{e}minaire de Math\'{e}matiques Sup\'{e}rieures is an annual graduate summer school funded by various mathematics research institutes across Canada and the United States. In 2016, SMS was held at the University of Alberta with the general theme Dynamics of Biological Systems''. Over the course of two weeks, twelve individual sessions were run on topics ranging from pattern formation and network symmetry to models of membrane electrical behavior and interacting populations.
In this talk, we will discuss the session on the modeling of infectious disease presented by Dr. Zhilan Feng (Purdue University). In particular, we will explore the effect of heterogeneous mixing of a population under a vaccination program and the coupling of within-host and between-host systems. Along the way, we will also present the necessary background to understand and enjoy the material.

Speaker: Ana Dias (November 15)
Title: Combinatorial Game Theory
Abstract: Combinatorial Game Theory is a branch of mathematics that studies strategies and mathematics of two-player no-chance games of perfect knowledge. These are games in which two players alternate moves, chance is not involved, and the state of the game and the set of available moves is always known by both players. In this talk we will take a look at some of these games which can be analyzed mathematically for optimal play. Some of the games we will talk about are: Nim games, Chomp, Hackenbush, and Omega.

Speaker: Tim Rey (November 22)
Title: An Overview of Advanced Analytics in Modern Industry
Abstract: Modern day industrial Advanced Analytics includes a blend of people, process, methods and technology. This talk will be an overview of such an environment and will include its future trends.

Speaker: Tibor Marcinek (November 29)
Title: Getting to know GeoGebra (better)
Abstract: Framed by an exploration of conic sections, we will sample various tools, commands and representations in GeoGebra. We will see how plane geometry, algebra (CAS), and space geometry representations interconnect and work together in GeoGebra. We will even put anaglyph glasses on!
Mathematically, we will not be going beyond pre-calculus. The pace will be gentle enough for GeoGebra beginners to follow but will also include advanced functionality hoping that even seasoned GGB users can learn something new.
Participants will be working at computers in the Mac Lab. If you prefer to work on your laptop, please install GeoGebra prior to the talk, it's free. (Click here to download ) Please make sure to install desktop software (Windows or Mac OS X or Linux). Although Chrome and tablet apps provide good functionality, the layout is different and will make it difficult to follow along.

Speaker: Matthew Moore (December 6)
Title: A Mathematical model of communication between cells to determine the tip/stalk fate
Abstract: The tip/stalk cell fate decision in blood vessel growth is a growing and active research field in both biology and mathematics. This talk will introduce a mathematical model of endothelial cells in the tip/stalk fate decision process modulated by the proteins, Notch and Delta. Researchers have observed that the Delta ligand has two activities; trans-activation of Notch receptors in neighboring cells and cis-inhibition of Notch within its own cell. High Delta and low Notch forms a tip cell, conversely, low Delta and high Notch will produce a stalk cell. In this talk, we will introduce the role of the Notch receptor and the Delta ligand in the cell. Second, we will describe the mathematical model. Third, we summarize the sensitivity analysis of signal in response to Delta production rate. Finally, we demonstrate how these proteins determine the tip/stalk fate between two cells when the Delta production rates are different.