Mathematics Department Colloquium: The Partitionability Conjecture

Colloquium | October 5 | 4:10-5 p.m. | 60 Evans Hall

 Caroline Klivans, Brown University

 Department of Mathematics

In 1979, Richard Stanley made the following conjecture: Every Cohen-Macaulay simplicial complex is partitionable. Motivated by questions in the theory of face numbers of complexes, the conjecture sought to bridge a combinatorial condition and an algebraic condition. Recent work of the speaker and collaborators resolves the conjecture in the negative. I will discuss the history and context of the conjecture, the counterexamples, the consequences, and the new questions we are now asking.