Graduate Student Advisory Committee (GSAC) Colloquium

Organizational meeting

Hilbert's syzygy theorem

In a module over a ring the generators do not have to be independent. We'll look at the relations of these generators and the relations of the relations, called syzygies. Over a hundred years Hilbert proved, that this process stops after n steps over a polynomial ring in n variables.

Magic Squares

The legend goes that an ancient land was being ruined by floods, and no sacrifices to the river god could stop the flooding. After each flood, a giant turtle would lumber onto land, examine the sacrifices, and slip back into the river, displeased. It was not until a child noticed the dots on the turtle's back that the people could stop the flooding; the turtle had a three by three grid of numbers, with the sum of each row equal and equal to the sum of each column. In this talk we will discuss magic squares, on and off turtles, and try to count the number of n by n squares with row sum k.

Specht modules for the symmetric group

The symmetric group over n elements is the set of permutations of these n elements. This seems pretty simple, but this group has n! elements, and its elements do not commute for n >2. A way to better understand a group G is to study its representations (or G-modules). In this talk, we'll construct all the building blocks (irreducible G-modules) for the symmetric group, using tables filled with integers.

What's an elliptic curve and why should I care?

Elliptic curves are among the most interesting and well-studied objects in all of mathematics. I will explain how elliptic curves can be used to solve problems ranging from ancient Greece to modern cryptography.

Tuning: It's easy as 41, 72, 53 or simple as do-re-mi

Let's start at the very beginning, a very good place to start. When you read, you begin with A-B-C. When you sing, you begin with do-re-mi. When you are designing a good tuning system, you begin by computing 5, 7, 12, 19, 22, 31, 41, 53, and 72 in several ways. In this talk, I will discuss the connection between number theory and algebra in musical tuning systems.

Equity and Performance Evaluation based Algorithm to address Pay Compression/Inversion

Pay compression and inversion are significant obstacles faced by many corporate and government entities for employee retention and equitable pay distribution. Compressed wage differentials within grades, often exacerbated by new hires being paid at similar or higher rates than employees with longer time in grade has been a particularly severe problem at Salt Lake County. This talk will discuss the Compression Ratio and Performance Evaluation based compensation algorithm that was used to address the problem in Summer 2018.

Continued Fractions and the Minkowski Question Mark Function

The Minkowski question mark function, denoted ?(x), is a natural example of a singular function - a continuous, 1-1, onto, and strictly increasing function whose derivative is zero almost everywhere. It turns out that its construction is intimately related to the continued fraction algorithm, an alternate way of expressing real numbers that has surprising connections to a wide variety of fields of math. In this talk, we will show how to find a number's continued fraction expansion and discuss some of the algorithm's number theoretic properties before defining the Minkowski question mark function and exploring its relationship with continued fractions.

Do we know all the numbers?

How many cells are in our body? What is the speed limit in Montana? How can we find bigger primes? What is love? Baby don't hurt me. These and many other questions won't be answered in this talk due to lack of knowledge of the speaker. Instead, we will present how language and time limit our approach to numbers, going from natural numbers to real numbers, and finishing with Abel's impossibility theorem about how we can write algebraic numbers.

A Mathematical Model Of The Zombie Apocalypse

If (when?) a zombie outbreak occurs, will we be prepared? Could humanity survive such an epidemic? Can we apply measures that might slow or stop the spread of the zombie infection? Gathering assumption from pop-culture and exploring several intervention tactics, we explore the zombie epidemic using a modified version of the classic SIR model of infectious disease.

AWM professor panel

Looking for a research advisor? Or just curious to hear what research is done in our math department? Come hear six professors/potential advisors from various fields of math explain what interests them most in their research, and meet them over snacks. Our speakers will be, by alphabetical order:

• Thomas Alberts
• Harish Bhat
• Fernando Guevara Vasquez
• Srikanth Iyengar
• Dragan Milicic
• Karl Schwede

The adaptive immune response

Our adaptive immune system facilitates highly specialized attacks on disease causing particles called pathogens. After making friends with a few immunologists, I have reason to believe that part of the adaptive immune system responds non-monotonically to changes in initial levels of pathogen. This is counterintuitive and motivates the need for mathematical modeling. Will a system of ODEs be enough to capture the complexities of the adaptive immune response? Will stochastic processes make an appearance? Will I be able to convince my new friends of the importance of mathematical modeling? Stay tuned.

Zombie Apocalypse: A Thanksgiving, Graph Theoretic Edition

Have you ever thought to yourself: What if there is a zombie apocalypse and I need to discover the outcome using mathematics? If you were a sensible human being you'd use differential equations as presented earlier this year in GSAC. However, for this talk, we assume we exist in realm without differential equations and so instead formulate this problem using graph theory. We shall explore a field of graph theory called Pebbling and use these results to save the humans or find out when we're doomed. All with a Thanksgiving twist of course!

Queer Mathematicians: They’re Pretty Cool

Note the unusual date: Wed. Nov. 28.
Do you ever think to yourself as you’re reading a paper, “Gee, I wonder if this author is gay?” I don’t, but that doesn’t mean that cool queer mathematicians don’t exist. Although the personal lives of mathematicians, and scientists in general, are not typically involved directly in their work, there have been some high profile queer mathematicians. We’ll take a quick trip through the personal lives and mathematical contributions of some famous ones of the past, such as Paul Erdős, G. H. Hardy, and, of course, Alan Turing, and end with a highlight of some contemporary queer contributions.

Special AWM Discussion

Utah's student chapter of the Association for Women in Mathematics is pleased to announce the Fall 2018 lecture of our Speaker Series. This series brings prominent female mathematicians from across the country to Utah to share their career experiences. Come learn about Dr. Thomases' career path and experiences as a mathematician. This special talk will consist of an open discussion of career issues in mathematics. All are welcome to attend. Come with questions!