# Graduate Student Advisory Committee (GSAC) Colloquium

**(**

Tuesdays, 4:35–5:35 PM, JWB 335

Math 6960–001

## Graduate Colloquium

Fall 2017Tuesdays, 4:35–5:35 PM, JWB 335

Math 6960–001

*credit hours available!*)

GSAC Home | Past Graduate Colloquia

The goal of this Colloquium is to encourage interaction among graduate students, specifically between graduate students who are actively researching a problem and those who have not yet started their research. Speakers will discuss their research or a related introductory topic on a level which should be accessible to nonspecialists. The discussions will be geared toward graduate students in the beginning of their program, but all are invited to attend. This invitation explicitly includes undergraduate students.

## Special AWM Discussion with Moon Duchin

Moon DuchinNote the unusual date: Wednesday Aug 30, 4:35 pm, in JWB 335.

Utah's student chapter of the Association for Women in
Mathematics is pleased to announce the second lecture in a recently
established lecture series. This series brings prominent female
mathematicians from across the country to Utah to share their career
experiences. This special talk will consist of an open discussion of
career issues in mathematics. All are welcome to attend. Come with
questions!

## Limitations of a ruler and compass

Derrick WigglesworthIn this talk we'll discuss what we can (and can't) do with a ruler and compass. We will begin by exploring what is meant by "a ruler and compass construction." By the end of the talk, we will prove several famous theorems, like the impossibility of squaring the circle, and the impossibility of trisecting an angle. I intend to make this talk accessible to anyone who has had a high school geometry class.

## What do rings of smooth functions look like?

Vaibhav PandeyWe consider the ring of smooth functions defined on [0,1] or the circle, and try to understand how the smoothness of these functions and topology of the ambient space impacts the ring structure. So, we will be working in the intersection of algebra, analysis and topology!

## Topological Types of Algebraic Curves

Leonard CarapezzaPart of Hilbert's 16th problem asks how many topological types there are of real algebraic curves of fixed degree in the real projective plane. In this talk I'll discuss how to think of real algebraic curves as living in the real projective plane, what is meant by topological type and what/how progress has been made on this problem.

## Is the Grass Greener on the Other Side?: Adventures in Optimal Foraging

Samantha HillNote the unusual date: Thursday Sep 28, 4:35 pm, in JWB 335.

Suppose that this morning you woke up to find that you were, in
fact, a beetle. As you fly around patches of plants, you must decide: for
how long should I visit this plant? Is the grass really greener in the
other patch? In this mathematical ecology talk, we will explore the
behavior of an optimal forager in response to different levels of
palatability in a plant community. A guest appearance will be made by the
Marginal Value Theorem.

Here are the slides of the talk.

## Employment Opportunities at the Department of Defense (in which we discuss RSA encryption)

Casey Johnson - Department of DefenseWe discuss at a high level a variety of security-related positions within the U.S. Government that may be of interest to mathematicians. This will include professional opportunities, as well as internships available to graduate students. We will also discuss the RSA cryptosystem, with an overview of quantum computing's potential for altering the landscape of public-key cryptography.

## The Farey Graph and Applications to Continued Fractions

Kristen LeeThe Farey graph can be constructed inductively using a simple rule of mediants. We will discuss how this particular construction applies to continued fractions leading to an alternate method of construction. Special appearances will be made by the Fibonocci sequence, the quadratic formula, and the golden ratio. A basic understanding of how to add fractions incorrectly is recommended but not required.

## Lost in a Forest and Random Walks

Jenny KenkelNote the unusual date: Thursday Nov 1, 4:35 pm, in JWB 335.

Groggily, you open your eyes. Above you are tall, dark trees,
and below you are wet, dead leaves. You realize you're in a forest, with
no memory of how you got there. Suddenly, an image flashes in your mind:
the precise shape and dimensions of this forest. What is the optimal path
to take to leave the forest? And what if... you're not alone?

## On the rheology of cats: are cats fluid?

Anna NelsonIn this talk we will determine whether the claim that cats are liquid is solid! Using principles of rheology and fluid mechanics, we will study the flow and deformation of cats in different time scales. No prior knowledge of fluid mechanics is required!

## HFT Implementations of Quantitative Strategies

Prem NarayananHigh Frequency Trading is the system of Algorithm based trading programs that move in and out of positions very quickly. Positions are held briefly, usually for fractions of a second to try and make profits out of very small changes in price. By some estimates, over 60% of all trading volume is algorithmic. Algorithmic execution of block trades is an important tool allowing for systematic execution of orders. We will take a look at some implementations of quantitative strategies such as Statistical Arbitrage that are used for HFT.