### Translational scissors congruence

- Series
- Geometry Topology Seminar
- Time
- Monday, May 13, 2019 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Inna Zakharevich – Cornell

One of the classical problems in scissors congruence is

this: given two polytopes in $n$-dimensional Euclidean space, when is

it possible to decompose them into finitely many pieces which are

pairwise congruent via translations? A complete set of invariants is

provided by the Hadwiger invariants, which measure "how much area is

pointing in each direction." Proving that these give a complete set

of invariants is relatively straightforward, but determining the

relations between them is much more difficult. This was done by

Dupont, in a 1982 paper. Unfortunately, this result is difficult to

describe and work with: it uses group homological techniques which

produce a highly opaque formula involving twisted coefficients and

relations in terms of uncountable sums. In this talk we will discuss

a new perspective on Dupont's proof which, together with more

topological simplicial techniques, simplifies and clarifies the

classical results. This talk is partially intended to be an

advertisement for simplicial techniques, and will be suitable for

graduate students and others unfamiliar with the approach.