Junior Colloquium Schedule
Donald Pfaff - UNR
Thursday, April 24, 2:30 in AB206
Title: If circles were squares...
Abstract: Since a circle is defined solely in terms of distance, if we changed
our definition of distance, the figure known as a circle would look different, as
would other figures such as ellipses, parabolas and hyperbolas. We will define
a reasonable distance so that circles are squares. What will ellipses look like?
Will the obvious answer, rectangles, be correct? Or will the answer be, like
all obvious answers to Pfaff’s questions, wrong? Be sure to come and see the
exciting answer to this and, as time permits, other questions.
Chris Wingard - UNR
Tuesday, April 15, 2:30 in AB206
Title: Dangers of the Infinite: Cantor and His Legacy
Abstract: Are there as many real numbers between 0 and 1 as there are between 0 and 3? Are there as many even integers as integers? As many integers as real numbers? The answers to some of these questions may surprise you. We will explore the answers to these questions, some similar questions, and the theory behind them, seeing along the way the different levels of infinity. Georg Cantor, considered to be the father of set theory, was the first mathematician to do real research dealing with the infinite. We will hear bits and pieces of his tragic tale and discuss some of some of his most surprising results and ideas, including the ever-elusive continuum hypothesis. Afterwards we examine the seven (sometimes eight) axioms which form the basic foundation for all of mathematics, and we will see how the logicians Kurt Gödel and Paul Cohen continued Cantor’s work. We conclude with the answer to the question posed by the continuum hypothesis and mention some related ideas and results.
Prerequisite for understanding: A strong desire to learn about something so fascinating, it should be illegal. It would help to know some very basic set theory, but such knowledge is by no means necessary.
Paul Kirk - Indiana University
Monday, November 19, 5:30 in AB638
Title: Some comments on the Poincaré Conjecture
Abstract: Perelman recently settled the famous Poincaré conjecture and the geometrization conjecture. I'll explain what the conjecture says, give a little history, some examples, and the briefest outline of how Perelman approached and solved the problem.
Michael J. Adams - Truman State University
Monday, October 22, 1:00 in AB634
Title: Graphs, Linear Algebra, and Ecology
Abstract: The connections between graph theory and linear algebra, and between linear algebra and ecology, are well-established. There is also a small but growing body of literature built around applications of graph theory to ecology: one such application is a technique known as demographic loop analysis. In this talk I will describe recent work in loop analysis in which graph theory, linear algebra, and ecology come together in a beautiful and surprising way. This talk should be accessible to anyone with a basic undergraduate background in calculus and linear algebra.