If we have a map of New York State then we know that every point in New York is represented by a point on our map. If we place our map on the ground and pair up every point on the map with the point on the ground that it touches, will there be a spot that gets paired with the exact spot on the ground that it is supposed to represent?
In this talk we will discuss the Brouwer Fixed Point Theorem which answers this question and how algebraic topology can be used to prove it. This talk is accessible to anyone who has seen one semester of calculus.
David Rosenthal is currently a graduate student at Binghamton University where he is finishing his Ph.D. in algebraic topology. He received his Bachelors Degree in 1996 and his Masters Degree in 1998 from Binghamton University. He is a fellow in the "Preparing Future Faculty" program in the Department of Mathematical Sciences.