## Invited Speakers

**Robert L. Devaney**

Robert L. Devaney is currently Professor of Mathematics at Boston University. His main area of research is dynamical systems, primarily complex analytic dynamics, but also including more general ideas about chaotic dynamical systems. He received his PhD from the University of California at Berkeley in 1973 under the direction of Stephen Smale. 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 35 countries on six continents worldwide. (He only needs Antartica to complete his goal of speaking on all continents ---so if you teach at South Pole State and run some kind of seminar, give him a call!) He is currently serving as the President of the MAA.

**Ravi Vakil**

Ravi Vakil is a Professor of Mathematics at Stanford, where he is also the Robert K. Packard University Fellow and the David Huntington Faculty Scholar. He is an algebraic geometer, and his work touches on many other parts of mathematics, including topology, string theory, applied mathematics, combinatorics, number theory, and more. He was born in Toronto, Canada, and studied at the University of Toronto, where he was a four-time winner of the Putnam competition (“Putnam Fellow”). He received his Ph.D. from Harvard in 1997, and taught at Princeton and MIT before moving to Stanford in 2001. He has received the Dean's Award for Distinguished Teaching, the American Mathematical Society Centennial Fellowship, the Frederick E. Terman fellowship, an Alfred P. Sloan Research Fellowship, the NSF CAREER grant, and the Presidential Early Career Award for Scientists and Engineers. He has also received the Coxeter-James Prize from the Canadian Mathematical Society, and André-Aisenstadt Prize from the CRM in Montréal. He was the 2009 Earle Raymond Hedrick Lecturer at MathFest, and is the Mathematical Association of America's Pólya Lecturer 2012-2014. He has served as an informal advisor to the new website mathoverflow. He works extensively with talented younger mathematicians at all levels, from high school (through math circles, camps, and olympiads), through recent Ph.D.'s.

**Skip Garibaldi**

Skip Garibaldi is associate director of the Institute for Pure and Applied Mathematics (IPAM) at UCLA and a professor in the Department of Mathematics & Computer Science at Emory University. Skip’s main area of research is on linear algebraic groups and cohomological invariants in Galois cohomology, but he has written papers on a remarkably diverse range of mathematics including the birthday problem, the uses and mis-uses of the Lie group E8 in physics, how much a governor should know about trigonometry, and finding good bets in the lottery, which won the Lester R. Ford Award in 2011. Millions of people have seen him talk about the lottery and his work on 20/20, CNN, ABC World News, and Fox & Friends, and he is featured in a museum exhibit about mathematics that is traveling the country.

## Talk titles and abstracts:

**Skip Garibaldi**

*Friday evening banquet talk:*

Math and the lottery: answers to good questions from students and reporters

I never thought much about the lottery until I taught a course on finite probability and the students asked me: "Why shouldn't we buy lottery tickets?" That is a much more complicated question than it first appears. Answering it led to more conversations with students and to interviews with reporters, and more good questions. In this talk, I will describe some of the more interesting questions and their answers.

**Robert L. Devaney:**

*Thursday evening, June 26, 8:00pm in ISB 110:*

Chaos Games and Fractal Images

In this lecture we will describe some of the beautiful images that arise from the "Chaos Game." We will show how the simple steps of this game produce, when iterated millions of times, the intricate images known as fractals. We will describe some of the applications of this technique used in data compression as well as in Hollywood. We will also challenge students present to "Beat the Professor" at the chaos game and maybe win his computer.

*Friday afternoon, June 27, 1:20pm in ISB 110:*

The Fractal Geometry of the Mandelbrot Set

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.

**Ravi Vakil:
**

*Friday, 9:00am ISB 110
*

Lecture A: The mathematics of doodling

Doodling has many mathematical aspects: patterns, shapes, numbers, and more. Not surprisingly, there is often some sophisticated and fun mathematics buried inside common doodles. I'll begin by doodling, and see where it takes us. It looks like play, but it reflects what mathematics is really about: finding patterns in nature, explaining them, and extending them. By the end, we'll have seen some important notions in geometry, topology, physics, and elsewhere; some fundamental ideas guiding the development of mathematics over the course of the last century; and ongoing work continuing today.

*Saturday, 10:45am ISB 110*

Lecture B: Murphy's law in geometry

When mathematicians consider their favorite kind of object, the set of such objects often has a richer structure than just a set --- often some sort of geometric structure. For example, it may make sense to say that one object is "close to" another. As another example, solutions to equations (or differential equations) may form manifolds. These "moduli spaces" often are hoped to behave well (for example be smooth). I'll explain how many ones algebraic geometers work with are unexpectedly as far from smooth as they possibly can be.

College of Humanities & Sciences