Spring 2012, Thursdays, Milner 216, 4:00-4:50 PM

Date: March 21

"  Ellipses and Pendulums and Groups, Oh My! From Elliptic Integrals to Elliptic Curves "
  Prof. Edray Goins   Purdue University


While a student in the Italian city of Pisa, Galileo Galilei became interested in a suspended lamp swinging back and forth in a cathedral. He began taking notes on the phenomenon in 1588, then conducting experiments in 1602, where he derived an empirical formula which related the period of the motion with the weight of the lamp. After Sir Isaac Newton's 1671 publication of his theory of Fluxional Calculus, mathematicians were able to derive a precise formula for the period using integrals. These integrals caught the interest of mathematicians, as they could not be evaluated in terms of well-known functions of the day. By 1751, Leonhard Euler had generalized results of Giulio Fagnano from the previous year by showing that there exists a remarkable addition formula for these integrals. The study of these ``elliptic integrals'' eventually led to the study of ``elliptic curves.'' In this talk, we discuss the genesis of elliptic curves through a historical perspective. We discuss some of the well-known results in the field, and end with some open problems of interest to graduate students wishing to pursue study in the area.