Mathematics Program Presents
Locally Determined, and Not Locally Determined, Invariants of Polyhedra
Thursday, February 23, 2017
Hegeman 308
4:45 pm EST/GMT-5
4:45 pm EST/GMT-5
Ethan Bloch
Mathematics Program
Mathematics Program
A very useful number associated with polyhedra is the Euler characteristic, which in the 2-dimensional case is V - E + F, where V, E and F are the number of vertices, edges and faces of a polyhedron, respectively. In this talk we consider the question of whether the Euler characteristic is locally determined, which means that it can be calculated as the sum of numbers determined in a neighborhood of each vertex of the polyhedron; there are combinatorial and geometric versions of this question, where the geometric version goes back to an idea of Descartes, from before Euler. We will then ask the analogous
question regarding the Charney-Davis quantity of a polyhedron, which in the 2-dimensional case is 1 - (1/2)V + (1/4)E - (1/8)F. This talk should be suitable for all students who are currently in Math 261 (Proofs and Fundamentals) or beyond.
Refreshments to follow immediately in the Mathematics Common Room
For more information, call 845-758-7104, or e-mail [email protected].
Time: 4:45 pm EST/GMT-5
Location: Hegeman 308