## UIC Graduate Student Seminar

Friday September 7
3:00 pm
636 SEO

Speaker: Brayton Gray

Title: The Ham Sandwich Theorem

Abstract: Topology concerns itself with qualitative questions rather than specific solutions. A good example of this is the intermediate value theorem from calculus: if f is continuous, "a< b", "f(a)<0", and "f(b)>0", then for some x between a and b, f(x)=0. The main topological feature here is continuity. We imagine moving x from a to b and watching f(x) move. Suppose we have a piece of ham on a plate and we would like to cut it in half. The intermediate value theorem tells you that there is a place to cut so that each side will be half. Now suppose that you have a piece of ham and a hunk of cheese and a bit of bread all arranged in some arbitrary way in front of you. Is there a way with one chop to split this so that each side has the same amount of ham, the same amount of cheese, and the same amount of bread? Come and find out, and how topology shows the answer.