Graduate Student Advisory Committee (GSAC) Colloquium

Special AWM Discussion with Moon Duchin

Note 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

In 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?

We 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

Part 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

Note 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)

We 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

The 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

Note 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?

In 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

High 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.

Uncertain??? You Have No Idea!

Data assimilation (DA) methods exists because all of our information is approximate. The basic idea of DA methods is to combine information on the quantity of interest from multiple sources, thereby (ideally) reducing the uncertainty of the final estimate. However, DA methods can only mitigate the sources of uncertainty that we have identified, the known unknowns. While we can never grasp the scope of the unknown unknowns, we can talk about what we know we do not know, and we shall! Join me in this math history and philosophy talk as we build from first principles the necessary assumptions required for DA methods to exist and be useful. Along the way we will meet some of the mathematicians and philosophers whose ideas led us to our current understanding of our own uncertainty.

Finite and Infinite Hat Problems

You and your friends got kidnapped by a villain, who has a challenge for you. He randomly gives you a hat of a certain color, that you cannot see, but you can see your friends' hats. You have to guess your hat color, or pass. If at least one person guesses correctly, and no-one guesses incorrectly, you are all free! Otherwise... you might all be eaten by the villain! We will talk about the best strategy to be free! What if now you are not allowed to guess? And what if you need to guess correctly your own hat color to be free? How many of your friends (and you?) can be saved? We will also consider the case where you are lucky enough to have infinitely many friends! This talk will involve (a tiny bit of) abelian groups, probability, logic/set theory, and graph theory, but should be accessible to anyone who knows what an equivalence class is.

Graduate Student Forum on Teaching

This event is an open dialogue with Kelly MacArthur for feedback, questions, and concerns about the teaching requirement for PhD students. The goal of this dialogue is to discuss things that are or are not working, and how the department might improve things going forward. This is also an opportunity to ask why the department does things in a certain way (for example, ""Why are the classes so tightly supervised/coordinated?"), assuming that Kelly knows the answer. If you're nervous to voice a particular opinion or you have a question that you don't feel comfortable asking in front of everyone, please write your comment or question on a sheet of paper and put it in Kelly's box anonymously.