$\vec{w}h\alpha\mathfrak{t}\;\; i\mathbb{S}\ldots$

the Euler characteristic of a polytope?

Hannah Sjöberg (FU Berlin)
2019/11/09, 13:00
Before the BMS Friday Colloquium by Prof. Raman Sanyal
Urania Berlin, at Newton room (2nd floor)
About what?

The Euler characteristic of a non-empty (solid) polytope $P$ is the alternating sum of the number of non-empty $i$-dimensional faces of $P$. The Euler-Poincaré formula asserts that this alternating sum is equal to $1$. In this talk we discuss how the Euler characteristic can be constructed as a valuation. The construction has nice applications: we will see that it gives us simple proofs of the Euler-Poincaré formula and of a theorem on the number of regions in a hyperplane arrangement.