Monday 23 March 2026
14:30–16:00*

Cary Malkiewich (Binghamton University) — Higher scissors congruence

Scissors congruence is the study of polytopes, up to the relation of cutting into finitely many pieces and rearranging the pieces. In the 2010s Zakharevich defined a "higher" version of scissors congruence, where we don't just ask whether two polytopes are scissors congruent, but also how many scissors congruences there are from one polytope to another. (This forms a moduli space!) Zakharevich's definition is a form of algebraic K-theory, which is famously difficult to compute, but I will discuss a surprising result that makes the computation possible, at least in low dimensions. In particular, this gives the homology of the group of interval exchange transformations, and a new proof that Thompson's group V is acyclic. Much of this talk is based on joint work with Anna-Marie Bohmann, Teena Gerhardt, Mona Merling, and Inna Zakharevich, and with Alexander Kupers, Ezekiel Lemann, Jeremy Miller, and Robin Sroka.

* Eastern European Time, i.e. UTC+2 in winter and UTC+3 in summer.