Mathematics Program Presents
From the Ham Sandwich to the Pizza Pie:
An Introduction to Topological Combinatorics
Thursday, March 30, 2017
Hegeman 308
4:45 pm EDT/GMT-4
4:45 pm EDT/GMT-4
Steve Simon, Mathematics Program
Given any 3 shapes in R3 (e.g., a piece of ham, a hunk of cheese, and a slice of bread), does there exist a single plane that simultaneously cuts each shape into two pieces of equal volume? Can any shape in R2 be dissected into four pieces of equal area by some pair of perpendicular lines? By exploiting hidden geometric symmetries, we will show how equipartition problems such as these can be solved using powerful techniques from the seemingly unrelated eld known as algebraic topology. For instance, the positive answer to the rst problem above { the so-called Ham Sandwich" Theorem { ultimately reduces to a very deep result of Borsuk and Ulam: for any continuous map from a sphere to a plane, there must exist a pair of antipodal points on the sphere whose images coincide. While fairly advanced mathematics is not too far away, this talk requires only a familiarity with the intermediate value theorem to be understood. All are welcome to attend!For more information, call 845-758-7104, or e-mail [email protected].
Time: 4:45 pm EDT/GMT-4
Location: Hegeman 308