Roever Lecture: Combinatorics of the Tautological Lamination

Abstract: Laminations arise in geometry whenever surfaces are manhandled - they parameterize the stretching or shearing or tearing of 2-dimensional fabrics. They arise in complex dynamics when one uniformizes the Fatou domain of polynomials via cut-and-paste. One complex dimensional slices of the parameter spaces of such polynomials are parameterized by *Tautological Laminations*. We describe one such lamination that arises in the parameterization of the Cubic Shift Locus, and explain its unexpected connection to a problem in combinatorics. This will be a general talk, and no previous knowledge of complex dynamics or combinatorics (or textile manufacturing) is required.

Host: Steven Frankel

Reception to follow at Cupples I, Room 200 (Lounge) from 2:00 - 3:00 pm.