# Undergrad Colloquium Winter 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

**Monday, January 19, 2015 *Martin Luther King Jr. Day* NO SEMINAR
**

**Monday, January 26, 2015**

**The Uniqueness of a Projective Plane of Order 4**

**Bruce Cooperstein, University of California, Santa Cruz**

We will illustrate ideas from incidence geometry in proving that there exists, up to isomorphism, a unique projective plane of order 4. In the course of the proof we will define what is meant by a projective plane as well as several other incidence geometries, including generalized quadrangle.

**Monday, February 2, 2015
** In this talk I'll describe a little bit of the fundamentals of Matrix Mechanics. This was a realization by physicists (most notably Heisenberg) that the weird behavior observed in very small particles could be understood through Linear Algebra. I'll discuss some very simple motivating experiments and explain how to predict its results. To finish, I'll explain fun things like Schrödinger's cat and mysterious things like entropy.

*Gabriel Martins,*

**Linear Algebra and Quantum Mechanics**

**University of California, Santa Cruz**

**Monday, February 9, 2015**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. In this talk we will present the history and some different routes mathematicians have used to tackle the outstanding problem. This talk is aimed towards sophomore and junior math majors. All are welcome.

The Collatz Conjecture

Juan Salinas

**Monday, February 16, 2015 *President's Day* NO** SEMINAR

**Monday, February 23, 2015**30 years ago Jean-Paul Allouche (Research Director, CNRS) began to investigate a curious class of infinite products which arose in relation to number theory. These are infinite products of rational functions taken to the power of an Automatic Sequence; a sequence generated by a finite automaton, or a model of a simple computer. Both the behavior of these sequences and the related products can be quite wild. One sequence in particular can be represented as the sequence of peaks in a folded piece of paper.

Infinite products arising from paperfolding

Hadrian Quan, University of California, Santa Cruz

In this talk I’ll describe how great undergraduate research can be, and give some calculations of infinite products. Although an undergraduate calculus course may venture into discussion of infinite series, infinite products can be even more exciting

**Monday, March 2, 2015
**

*Gender in Mathematics*

**Laura Wisdom, University of California, Santa Cruz**

The stereotype that women are not as capable at mathematics as men has long been proven false, but still impacts many mathematical institutions today. At UCSC, not a single area of the mathematics department (undergrad, grad student, or faculty) has a 50/50 gender split. I'll discuss possible reasons for this, gender bias at all levels of university and pre-university education, and positive feasible solutions. The purpose of this talk is to start a conversation about recognizing and combating gender bias in mathematics. Topics such as stereotype threat and safe-space principles will be addressed. All genders are welcome and encouraged!

**Monday, March 9, 2015**

**Monday, March 16, 2015**