The Fractal Geometry of Mandelbrot Set
Robert L. Devaney
Boston University
In this lecture we describe several folk theorems concerning the Mandelbrot set. While this set is extremely complicated from a geometric point of view, we will show that, as long as you know how to add and how to count, you can understand this geometry completely. We will encounter many famous mathematical objects in the Mandelbrot set, like the Farey tree and the Fibonacci sequence. And we will find many soon-to-be-famous objects as well, like the “Devaney” sequence. There might even be a joke or two in the talk.
A native of Methuen, Massachusetts, Robert L. Devaney is currently Professor of Mathematics at Boston University. He received his undergraduate degree from the College of the Holy Cross in 1969 and his PhD from the University of California at Berkeley in 1973 under the direction of Stephen Smale. He taught at Northwestern University and Tufts University before coming to Boston University in 1980.
His main area of research is dynamical systems, primarily complex analytic dynamics, but also including more general ideas about chaotic dynamical systems.
He is the author of over one hundred research papers in the field of dynamical systems as well as a dozen pedagogical papers in this field. He is also the (co)-author or editor of fourteen books in this area of mathematics.
In 2012 he will become President-elect of the Mathematical Association of America. Then, in 2013-14, he will serve as the President of the MAA.
Professor Devaney has delivered over 1,500 invited lectures on dynamical systems and related topics in all 50 states in the US and in over 30 countries on six continents worldwide. He has also been the “Chaos Consultant” for several theaters’ presentations of Tom Stoppard’s play Arcadia. And, in 2007, he was the mathematical consultant for the Kevin Spacey movie called Twenty One.
For the last twenty years, Professor Devaney has been the principal organizer and speaker at the Boston University Math Field Days. These events bring over 1,000 high school students and their teachers from all around New England to the campus of Boston University for a day of activities aimed at acquainting them with what’s new and exciting in mathematics.
In 1994 he received the Award for Distinguished University Teaching from the Northeastern section of the Mathematical Association of America. In 1995 he was the recipient of the Deborah and Franklin Tepper Haimo Award for Distinguished University Teaching at the annual meeting of the Mathematical Association of America. In 1996, he was awarded the Boston University Scholar/Teacher of the Year Award. In 2002 he received the National Science Foundation Director’s Award for Distinguished Teaching Scholars. In 2002, he also received the ICTCM Award for Excellence and Innovation with the Use of Technology in Collegiate Mathematics. In 2003, he was the recipient of Boston University’s Metcalf Award for Teaching Excellence. In 2004 he was named the Carnegie/CASE Massachusetts Professor of the Year. In 2005 he received the Trevor Evans Award from the Mathematical Association of America for an article entitled Chaos Rules published in Math Horizons. In 2009 he was inducted into the Massachusetts Mathematics Educators Hall of Fame. And in 2010 he was named the Feld Family Professor of Teaching Excellence at Boston University.
