**Professor John W. Milnor SUNY, Stony Brook**

**Wednesday, October 8, 1997, 4:00 p.m.
Physics Building, Room 202**

*"Pasting Together Julia Sets"*

This lecture will describe how one can paste together two rather skinny fractal sets, with no interior, to obtain a full 2-dimensional sphere. If f is a polynomial map from the complex numbers to themselves. then the "filled Julia set" K60 is the set of complex numbers z such that the sequence z, f(z), f ((fz)), . .. is bounded. This is usually a complicated fractal set. Yet the operation of "mating", which pastes together two such filled Julia sets to yield a smooth Riemann sphere, is often defined. The lecture will study one particularly non-intuitive example of this construction.

**Thursday, October 9, 1997, 4:00 p.m.
Boyd Graduate Studies Research Center, Room 328**

*"Understanding the Mandelbrot Set"*

The Mandelbrot set M can be thought of as the table of contents for a (very large) book which describes all possible kinds of dynamic behavior for quadratic polynomial maps. The various complicated geometric structures seen in M correspond to different types of behavior. This lecture will explain some of this structure by studying periodic orbits for quadratic maps.

**Friday, October 10, 1997 4:00 p.m.
Boyd Graduate Studies Research Center, Room 328**

*"Rational Maps"*

Exploration of the larger world of rational maps from the Riemann sphere to itself.