# Undergrad Colloquium Winter 2014

McHenry Building - Room 4130

Refreshments served at 4:45 - McHenry Building 4161

For further information please contact the Mathematics Department at 459-2969

**Here are the dates for upcoming talks. Check this page for updates regarding speakers and abstracts.**

**January 8, 2014: TBA**

**January 15, 2014: TBA**

**January 15, 2014: TBA**

**January 22, 2014**

*Visual solutions to binary quadratic forms*

Mitchell Owen, University of California, Santa Cruz

In this talk I will introduce and define the quadratic topograph, a visual algorithm for finding values of binary quadratic forms developed by John Conway.

**January 22, 2014**

*Visual solutions to binary quadratic forms*

Mitchell Owen, University of California, Santa Cruz

**January 29, 2014 **

**January 29, 2014**

*Basic Compass and Straightedge Constructions and a Few Triangle Constructions*

Yusuf Gören, University of Calfornia, Santa Cruz

We will start with finding a parallel/perpendicular line, bisectors to angles and sides, and other few basic constructions. Having them in our toolbox, we will try to construct some triangles where only few segments or angles are known. Anyone with an open mind and curiosity to explore basics of plane geometry.

*Basic Compass and Straightedge Constructions and a Few Triangle Constructions*

Yusuf Gören, University of Calfornia, Santa Cruz

**February 5, 2014: TBA**

** **

**February 12, 2014**

*What is Algebraic Geometry?*

Gabriel Martins, University of California, Santa Cruz

In this talk I'll try to explain using a lot of pictures and basic examples what is algebraic geometry and what type of problems it let's us solve.

**February 12, 2014**

Gabriel Martins, University of California, Santa Cruz

*What is Algebraic Geometry?*

Gabriel Martins, University of California, Santa Cruz

**February 19, 2014**

*Sums of Squares*

Michael Magee, University of California, Santa Cruz

I'll explain some of the things we know about writing a natural number as the sum of two or three square numbers.

**February 19, 2014**

Michael Magee, University of California, Santa Cruz

*Sums of Squares*Michael Magee, University of California, Santa Cruz

**February 26, 2014**

*Rational Distance Sets on Conic Sections*

**Shawn Tsosie, ****University of California, Santa Cruz**

A rational distance set is a set of points, in the plane, whose coordinates and pairwise distance is rational. Leonard Euler noted that there exists an infinite rational distance set on the circle. This leads to the question about other conic sections. Stanislaw Ulam and Paul Erdos considered the problem for general algebraic curves and conjectured that any irreducible algebraic curve that is not a circle of line has finite rational distance set. This talk will explain how to use elliptic curves to find rational distance sets on a parabola and hyperbola.** **

**February 26, 2014**

*Rational Distance Sets on Conic Sections*

**Shawn Tsosie,****University of California, Santa Cruz**

**March 12, 2014**

*A Very Short Introductory Course in Knot Theory*

**Felicia Tabing, ****University of California, Santa Cruz**

Come and learn knot theory with me! I will introduce basic definitions and different ways of telling knots apart.** **

*A Very Short Introductory Course in Knot Theory*

**University of California, Santa Cruz**