Floor functions appear in number theory, e.g. in expressions for the Riemann zeta function and in some proofs of quadratic reciprocity. Often these floor functions show up with different "dilation factors", so it is essential to understand how such dilated floor functions interact with one another. In this talk I will answer the question: when is the commutator of two dilated floor functions identically non-negative?

No background will be assumed. This work is joint with Jeff Lagarias and Takumi Murayama. Speaker(s): Harry Richman (UM)