Olivetti Club

Elise McMahonCornell University
Scissors congruence: cutting and pasting polygons

Tuesday, March 30, 2021 - 4:30pm

Hilbert's 3rd problem asks: "when can you take two polytopes, cut up one, and arrange the pieces to equal the other?". In two-dimensional euclidean space, the answer is if they have the same area. For three dimensions however, volume is not enough to separate the scissors congruence class, and the "Dehn invariant" is also required. Goncherov approached the problem by using the "Dehn invariants" to construct a complex, which he then also conjectured is related to the algebraic k-theory of C.