# Undergrad Colloquium Fall 2014

McHenry Building - Room 4130

Refreshments served at 4:45 - McHenry Building 4161

For further information please contact Richard Gottesman or call the Mathematics Department at 459-2969

**Wednesday, October 8, 2014**

**"The Jones Polynomial"**

**Felicia Tabing, UC Santa Cruz**

Ms. Tabing will introduce a few very basic knot invariants, leading up to the Jones Polynomial. She will discuss how to determine the Jones Polynomial, and give examples of knots it distinguishes, and knots it can't distinguish.

**Wednesday, October 15, 2014**

**"A Friendly Introduction to Number Theory"**

**Richard Gottesman, UC Santa Cruz**

This talk will give an introduction to one of the oldest areas of mathematics, the theory of numbers. We will show how a simple and elegant idea that does back to at least Euclid can be used to prove theorems about prime numbers and Fibonacci numbers. The only tools we will use are high school algebra and the power of pure thought.

**Wednesday, October 22, 2014
**Jackson Hsu, UCSC Undergraduate

*"More Topics in Knot Theory"*

I will talk about some different families of knots and links, the linking number of a two component link, the stick number of a general knot/link, and other knot theory topics. All levels of math are welcome.

**Wednesday, October 29, 2014
**By focusing on the family E:y^2=x^3+a, I will present strategies for determining the structure of the torsion subgroup of the Mordell-Weil group of an elliptic curve, E(K), over a quadratic field $K$. Generalizations of the Nagell-Lutz theorem and Mazur's theorem to curves defined over quadratic fields allows us to determine the full torsion subgroup of E(K) as one of at most three possibilities when $a$ is a square.

*"Torsion of Elliptic Curves Over Quadratic Fields"*Jody Ryker, University of California, Santa Cruz

**Wednesday, November 5, 2014
** University of California, Santa Cruz

*"Cal Teach and the Math Major"*Gretchen Andreasen, Cal Teach Director,

Do you have an interest in teaching as a career? If so, come find out how the Cal Teach program can help you explore teaching as a career, while at the same time satisfying some of your degree requirements. Cal Teach offers internships, advising, professional development, and teaching resources for math, science, and engineering majors who are interested in teaching at the middle or high school levels. All aspects of the program will be discussed, as well as how the Cal Teach internships can satisfy math degree requirements or education minor requirements, including the new STEM education minor.

There will be pizza for students attending the presentation.

**Wednesday, November 12, 2014** TBA

**Wednesday, November 19, 2014
**I will discuss some research being done at the University of Washington related to Inverse Problems for Electrical Networks. We will explore how linear algebra and graph theory can help us recover conductances on electrical networks given information about how the network acts on its boundary. I will also talk a little bit about how great it is to do research as an undergraduate.

*Molly Baird, UC Santa Cruz*

**"Medial Graphs and Recoverable Graphs"**

**Wednesday, December 3, 2014
**

*"Geodesics On Surfaces"*

**C**onnor Jackman, UCSC Math Graduate Student

This talk will start with intuition on some relevant terms and concepts (no background will be necessary beyond some calculus). Next we will use the Euler-Lagrange equations and Clairaut's theorem to describe behavior of geodesics on surfaces of revolution such as the paraboloid and cone. Finally I will state a few interesting classical and recent results concerning surfaces with closed geodesics.

**Wednesday, December 10, 2014
**

*"Research Experiences for Undergraduates"*

**Professor Debra Lewis and Molly Baird, UCSC and more!
**We will discuss REU’s: Research Experience for Undergraduates. These programs take place in the summer and give undergraduates the opportunity to get paid to do research. Several people who have participated in REU’s will share their experiences. We will also discuss the application process.

Snacks and refreshments will be served at 4:30 PM in the Tea Room, McHenry 4161