Algebra to Astrophysics via the Complex Numbers
Speaker: Catherine Beneteau, University of South Florida
Date & Time:
12:00 PM - 2:00 PM
O'Shaughnessy Science Center (OSS 313)
Abstract: If we want to model a flat surface, we have some options. For instance, we can use real numbers x and y, and obtain the usual Cartesian plane of coordinates (x,y). Another option is to consider complex numbers
z = x + i y, where i is a special number whose square is 1. Because of that particular property of the imaginary number i, we see right away that the polynomial z^2 + 1 factors in the complex plane. In fact, one of the most amazing properties of the complex numbers is that every ploynomial factors into linear factors. This is the famous Fundamental Theorem of Algebra. On a seemingly completely separate note, in the early 20th century, Einstein discovered that light passing close to a massive body, a large galaxy say, bends around it. In fact, if the galaxy lies between an observer and the light source, the observer might see several images, not just one light source. In this talk, I will discuss how and why these two amazing facts are related.
Biographical information: Catherine was educated in Canada, at McGill University, where she earned her bachelor’s and master’s degree in mathematics. Catherine obtained her Ph.D. in 1999 at the University at Albany, under the supervision of Boris Korenblum.
Catherine’s main research interest is in complex analysis. She is also very interested in mathematics education and in curriculum development issues.