# Graduate Student Advisory Committee (GSAC) Colloquium

**(**

Tuesdays, 4:35–5:35 PM, JWB 335

Math 6960–001

## Graduate Colloquium

Fall 2018Tuesdays, 4:35–5:35 PM, JWB 335

Math 6960–001

*credit hours available!*)

GSAC Home | Past Graduate Colloquia

## Organizational meeting

## Hilbert's syzygy theorem

Janina LetzIn 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

Jenny KenkelThe 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

Sabine LangThe 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?

Dan SmolkinElliptic 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

Allechar Serrano LopezLet'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

Prem NarayananPay 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

Peter McDonaldThe 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?

Jose YanezHow 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

Jake MadridIf (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

Amanda AlexanderOur 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.