# Graduate Student Advisory Committee (GSAC) Colloquium

**Graduate Colloquium**

Fall 2016

Tuesdays, 4:35–5:35 PM, JWB 335

Math 6960–001(

Fall 2016

Tuesdays, 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.

## Representation Theory and the Hydrogen Atom

Anna RomanovaA major accomplishment of representation theory has been its predictive power in quantum physics. In this talk, we will discuss a fundamental example of this powerful connection. Using only some basic tools from representation theory applied to the underlying symmetry group of the hydrogen atom, we can extract detailed information about the structure of the four quantum numbers describing the possible quantum states of the hydrogen atom. The first part of the talk will touch on the history of representation theory and explore how representation theory found its way to the forefront of 20th century mathematics and physics. Then we will build the tools necessary to understand this beautiful connection. No background in representation theory or quantum mechanics is necessary for this talk.

## Final Fantasy Is Really Hard

Matt SmithWhen trying to solve a problem, I often ask myself: Is this really difficult? Or am I missing something totally obvious? This is a question mathematicians have faced for hundreds of years. For many classes of problems which can be solved by computers, the answer is still unknown! We will use an infamous puzzle from the video game Final Fantasy XIII-2 to motivate examining puzzles from an abstract point of view. Along the way, we'll discuss algorithms, Turing machines, complexity theory, and the one million dollar problem of P vs NP.

Accompanying slides

## The price is right: gambling, financial derivatives, and arbitrage

Daniel LeeThere's no such thing as a free lunch...or is there? We'll explore particular gambling situations in which we can make a riskless profit (i.e., an arbitrage opportunity). Then we'll dive into the world of financial markets and apply much of the same reasoning there to price special investments called options. Prerequisite: You need to know what money is.

## One Size Does Not Fit All: Integral Projection Models in Ecology

Samantha HillIn a world populated entirely by clones, we might never have to think about heterogeneity. This is not that world. Size, age, and other traits that give structure to a population also influence survival, reproduction, and growth. In this talk, we will consider matrix population models, PDEs, and integral projection models (IPMs) as ways to describe the dynamics of heterogeneous populations. Some IPM examples we may look at include models of sea fan coral and Soay sheep populations.

## Cancer for Mathematicians: Finding the Beauty in Large, Complex Models

Liz FedakAn unpredictable, fascinating quasi-death-sentence that could strike any one of us: that's cancer. Yet, societal implications aside, are mathematical models of cancer growth, development and treatment truly of practical importance? Come up with your own answer as you learn about the many, many complications that plague theoretical oncologists, the strategies we've implemented to capture small amounts of information amidst overwhelming complexity, and why it's necessary for us to forego a tenet of mathematics ('simplicity is beautiful') in order to succeed.

## Equation-free modeling: nascent or nonsense?

Chris MilesThe most well understood behaviors of complex systems often come at a fine scale (particles, cells, individual people), but we are interested in the large scale behavior of the collection of these individuals. Traditionally, the applied math approach is to model the large scale behavior directly. From this, a natural desire arises: can we use our fine scale (microscopic) knowledge to predict large scale (macroscopic) behavior. In this talk, I'll present a recent attempt at answering this question: a computational framework called "equation-free modeling". In this framework, the macroscopic behavior of a system need not be known in any way (i.e. "equation-free") as the microscopic evolution is used to predict emergent behavior at the macroscopic level. We'll also briefly discuss how bifurcations are propagated and criticisms of the framework.

## Factoring Primes

Kevin ChildersA very nice property of the integers is the Fundamental Theorem of Arithmetic, which states that any integer can be factored uniquely into primes. We will explore some consequences of extending the usual integers to larger rings of integers, including the "factoring of primes." We will apply these ideas to a classical number theory question: how many ways can a given integer be written as the sum of two squares?

## DNA Methylation Dynamics: The Importance of Collaboration

Kiersten UtseyWhen we consider what influences our traits and risk for disease we often focus on the genetic code carried in our DNA. However, many modifications to our DNA influence our traits and disease risk without changing the genetic code. DNA methylation is one such modification. Since DNA methylation is not part of the genetic code, it is not copied when DNA is replicated. Yet somehow DNA methylation marks remain stable through DNA replication and cell division events. In this talk we will explore a classical model proposed in 1975 to explain this phenomenon. We will then consider recent biological findings and what those findings suggest for current modeling efforts.

## Venn Diagrams: Beyond Math 1030

Hannah HogansonIn Math 1030 we use circle Venn Diagrams to show relationships between sets and to analyze deductive arguments. However, circles are not the best choice of shape for representing all possible relationships between sets. From this simple starting point, many involved combinatorial questions quickly arise. In this talk we will make precise the definition of Venn Diagram, prove that no four-circle Venn Diagram exists, explore symmetry properties, and discuss current combinatorial research on Venn Diagrams. No graduate level math is required!

## The History of the Normal Distribution

Jenny KenkelThe Normal Distribution, sometimes called the Bell Curve or the Gaussian distribution, is one of the most recognized curves in math and science. Heights, IQ scores, errors in measurements, and stock prices have all been assumed to be Normally distributed, sometimes with disastrous consequences. This talk will discuss the first derivation of the Normal distribution, which was not by Gauss, it’s rediscovery decades later, and its rise to ubiquity.

## TBA

Rachel Pries (in conjunction with AWM)TBA

## Sloshing problems: how to solve PDEs using Calculus of Variations?

Chee Han TanImagine on a Sunday morning, you were about to sip a perfectly brewed coffee, but suddenly it spills over the coffee mug. Admit it, you must be wondering why nobody has yet to come up with a coffee mug design that avoids such catastrophic event. This is closedly related to sloshing problem, which is just a fancy word describing oscillations of the free surface of a fluid in a container. Not surprising at all, this problem involves solving a system of partial differential equations (PDEs), which could be a nightmare for mathematicians refusing to solve it numerically! We will explore an interesting concept of tackling such problem using Calculus of Variations, which is the main theme of this talk.

## How Deep Learning Can Make Hiring Decisions Better With Less Than Humans

Ben Taylor (Chief Data Scientist at HireVue)Ben Taylor is the Chief Data Scientist for a local Sequoia backed startup called HireVue. HireVue does digital interviewing so top 100 fortune companies (IBM, JPMorgan, etc..) can hire top talent more efficiently. In addition to providing an interview system for recording and managing there is a huge machine learning component as well. After capturing 10-20 minutes of a video interview and recording that to the cloud the computer is then able to essentially watch the interview and make decisions on how well the candidate is doing. Not only is this approach very competitive, but it is also competing directly against the human recruiters for some roles that review the same content. Come and learn about how deep learning will revolutionize your future, and how it is already making hiring decisions more accurate with less bias.