THE REES DISTINGUISHED LECTURER SERIES

Dr. Greg Lawler

Cornell University 

WHERE DOES A RANDOM TRAVELER VISIT?

Thursday March 13, 2003

3:30 - 4:30 205 Kirkbride Hall

Imagine a person traversing a rectangular grid, randomly choosing each next site from the neighboring sites. Suppose the walker paints each site that she visits red. After a long time, what does the set of red sites look like? Suppose another walker also traverses sites painting each site he visits blue --- is it possible for no site to be painted both red and blue? How does this change if the walkers make a point of not trying to visit sites already visited?

I will discuss these questions and show why "dimension" is an important quantity --- both the dimension of the space the walker is traveling and the "fractal dimension" of the set of sites visited.

This talk is intended for a general audience.

 

CONFORMAL INVARIANCE AND CRITICAL PHENOMENA

Friday March 14, 2003

3:30 - 4:30 104 Gore Hall

There are a number of models from statistical physics that have been conjectured to have limits that are in some sense "conformally invariant" in two dimensions. Examples are percolation and self-avoiding walks. There has been a lot of activity recently proving such results. I will give give a survey of recent work, with an emphasis on research of mine in collaboration with Oded Schramm and Wendelin Werner. No previous knowledge of statistical physics models will be presumed.

This is a lecture for a general mathematical audience.