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Colloquium, Spring 2006

Day: Thursday, April 27th Time: 4:00pm Place: BH 112 Title: Elliptic Functions and Integrals Speaker: Cody Pond, Western Washington University Abstract: In calculus we learn how to find the arc length of parameterized curves through integration.  While this process is very simple in the case of a circle, when applied to ellipses the result is an integral that has no closed form solution.  Variants of this integral are called elliptic integrals and occur in a variety of physical and mathematical contexts. From one of these contexts --- the period of a simple pendulum --- we can derive an elliptic integral whose inverse can be regarded as a doubly periodic function on the complex plane.  Such functions are called elliptic functions. In this talk, I will explore the relationship between elliptic integrals and elliptic functions, show direct methods for constructing elliptic functions as well as deriving some of their simple properties, and discuss the relationship between elliptic functions and results in number theory.