We are very happy to have Alex Zupan joining us from University of Nebraska. His title and abstract are below.

Title: Complex curves in CP^2 from the perspective of bridge trisections Speaker: Alex Zupan, University of Nebraska Date: Apr 7, 2021 Time: 3:30 PM Room: https://meet.google.com/frv-bgow-byi

Abstract: Peter Lambert-Cole and Jeff Meier revealed that bridge trisections of complex curves in CP^2 exhibit elegant structure: Every complex curve admits an inefficient shadow diagram (with respect to the standard genus one trisection) in which shadow arcs form a hexagonal lattice in the torus. Additionally, Lambert-Cole proved a combinatorial classification of symplectic surfaces in CP^2 : A surface that minimizes genus in its homology class is symplectic if and only if it admits a transverse shadow diagram. We prove a complex version of Lambert-Cole’s theorem, that a genus-minimizing surface in CP^2 is complex if and only if it admits a transverse hexagonal lattice diagram. In the process, we find infinite families of efficient hexagonal lattice diagrams for complex curves, and we give a combinatorial characterization of the symplectic isotopy problem in CP^2

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Neil R. Hoffman Assistant Professor Department of Mathematics 523 Math Science Building Oklahoma State University Stillwater, OK 74078-1058 405-744-7791 http://math.okstate.edu/people/nhoffman