# Undergrad Colloquium Spring 2015

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

** April 13, 2015 at 5PM** The Collatz Conjecture (The 3n+1 problem) is an open problem in number theory. Like most open problems in number theory, the Collatz Conjecture is easy to state but extremely difficult to prove. Our goal for this talk will be to introduce this outstanding conjecture. All are welcome.

An introduction to the Collatz Conjecture

Juan Salinas

**
April 26, 2015
Quaternions and sums of four squares
Richard Gottesman, UCSC Math Grad Student
**I will describe a number system called the Quaternions, which is a generalization of the complex numbers. I will then describe how to use this number system to prove that every positive integer is a sum of four squares.

** May 11, 2015 at 4 PM** Following Douglas Hofstadter's work in "Gōdel, Escher, Bach", we will introduce and discuss the infomal formal M-I-U system. While very simple in its design, this system is surprisingly deep and fun to explore. The reason it is also useful is because it allows us to discuss properties of formal systems in general, including those that were used by Gōdel in his famous incompleteness theorems. There is no prerequisite knowledge in logic required.

Can you do MU?

Dr. Frank Bauerle, Lecturer, UCSC Mathematics Dept.

** Monday, June 1st at 5:00 PM in McHenry 4130 (Colloquium Room)** If G is a graph, a minor of G is a graph obtained by either removing vertices, removing edges, or contracting edges. A useful way to characterize certain families of graphs is by specifying finite sets of graphs that cannot be minors of any graph from that family. Such graphs are called forbidden minors. A classic example of this is Kuratowski's theorem.

Forbidden Minors and Intrinsically Knotted Graphs.

Jamison Barsotti, UCSC Math PhD student

In the first part of this talk we will consider the Robertson-Seymour Graph Minor Theorem. We will see what it implies and what its limitations are. We will then look at Conway and Gordon's seminal result that links the world of Knot Theory with the world of Graph Theory. Lastly, the discussion will focus on current research that is inspired by both results.

No previous familiarity will be assumed and the talk should be accessible to any student that has an interest in mathematics.

Note: Food and Refreshments will be served 30 minutes prior in the tea room -- directly across from 4130.

Note: Food and Refreshments will be served 30 minutes prior in the tea room -- directly across from 4130.

**Monday, October 19th, 2015 **

*TBA*