NO, YOU CANNOT GET THERE FROM HERE !
Zoran Sunik
SUNY Binghamton
It is clear that we cannot get to the other side of the street by crossing it four times. It is also clear that if we walk on the plane in such a way that we only make right angle turns, and we alternate turns to the left with turns to the right, we will never get back to the original position.
In both examples above, we start in a certain initial configuration, follow certain rules that tell us how we can change our configuration, and try to reach a certain final configuration. In the former example it was impossible to get to the final configuration from the initial in the prescribed number of steps, and in the latter example it was impossible to get to the final configuration in any number of steps.
We will discuss more involved and more interesting examples of the same flavor as the two examples above. We will jump like grasshoppers, play several games (most of the games have initial configurations and follow some rules, and some final configurations are more desirable than others), break glass with some hooligans and help them understand the limits of their behavior, and more.
This talk is accessible at all levels.
Zoran Sunik is currently studying for a PhD at SUNY Binghamton with his research focused on Algebra. He received his B.S. in mathematics from St. Cyril and Methodius University in Skopje, Macedonia in 1991, and his M.S., also from St. Cyril and Methodius University, in 1995. He is a fellow in the "Preparing Future Faculty" Program in the Department of Mathematical Sciences.