Dean of the College Presents
Ham Sandwiches, Pizza Pies, and the Mass Equipartition Problem:
An Introduction to Topological Combinatorics
Friday, April 8, 2016
RKC 111
12:00 pm EDT/GMT-4
12:00 pm EDT/GMT-4
Steven Simon, Wellesley College
Can any three shapes in ℝ3 be simultaneously cut into two pieces of equal volume by a single plane? Can any shape in ℝ2 be dissected into four pieces of equal area by two perpendicular lines? By exploiting hidden symmetries, we will show how equipartition problems such as these (as well as a variety of other questions from combinatorial geometry) can be solved using techniques from the seemingly unrelated field of algebraic topology. For instance, the positive answer to the first problem above -- the so-called "Ham Sandwich" Theorem -- ultimately reduces to a deep result of Borsuk and Ulam: for any continuous map from a sphere to a plane, there must exist some pair of opposite points on the sphere whose images coincide. Although group theory, topology, number theory, and even Fourier analysis are all truly at play, no background in these fields is required to appreciate the fascinating interplay of the continuous and the discrete at the heart of topological combinatorics. All are welcome to attend!For more information, call 845-758-7266, or e-mail [email protected].
Time: 12:00 pm EDT/GMT-4
Location: RKC 111