Topology, Algebraic Geometry, and Dynamics Seminar (TADS): Combinatorial Diagrams for Lagrangians in CP^2

Speaker:  Sarah Blackwell, University of Virginia

Title:  Combinatorial Diagrams for Lagrangians in CP^2

Abstract:  "Triple grid diagrams" are combinatorial diagrams arising from the standard genus one trisection of the complex projective plane which encode three links simultaneously. Following from fundamental results in the theory of trisections [Gay-Kirby] [Meier-Zupan], triple grid diagrams naturally represent smoothly embedded surfaces in the complex projective plane. Previous work of the author, Gay, and Lambert-Cole showed that furthermore, these diagrams can represent Lagrangian surfaces in the complex projective plane, thus capturing geometric information combinatorially. In this talk we further study the combinatorial properties of triple grid diagrams, showing that all links can be realized as part of such a diagram, describing moves on diagrams, and developing a permutation representation for these diagrams. This is joint work with Aaron Mathis.

Time:  Friday, October 18, 1:30pm – 2:30pm

Place:  Exploratory Hall, room 4208