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Topology/Geometry Seminar

Sheaves and Continuation in Dynamics

Alex Dowling (Rutgers-New Brunswick)

Location:  Hill 705
Date & time: Tuesday, 14 November 2023 at 4:00PM - 5:00PM

Algebraic structures, such as the lattice of attractors, provide a computable description of global dynamics. In this talk, we discuss recent work on a sheaf-theoretic approach to their continuation. Sheaves are built from algebraic structures of dynamics, which track the algebraic data as systems vary. Sheaf cohomology is computed for several classical bifurcations, demonstrating its ability to detect and classify bifurcations. Computational analogues of sheaves, cellular sheaves, are shown to yield a converging numerical method to compute sheaf cohomology.

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