# 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.