Title : Euler's formula and (much) more
Speaker : Dan Zaffran (Fudan University)
Date : 2009. 2. 19 (Thu) 13:00
Place : E6-1 #2411
Abstract:
a cube has F=6 faces, E=12 edges and V=8 vertices. A pyramid
with a square base has F=5 faces, E=8 edges and V=5 vertices. Euler
discovered in 1750 that for these two cases, or for any other
polyhedron, F-E+V=2. He published the result, but he confessed that he
was not able to prove it! He found a proof one year later.
This celebrated "Euler's formula" is the starting point of many
results and conjectures in higher dimensions. I will explain some of
them, and focus on the surprising methods that have been used to solve
these problems: topological manifolds and their algebraic topology,
cutting-edge algebraic geometry...