Fri, 26 Apr 2024
15:00 - 16:00
Patricia Dietzsch
ETH Zurich


This talk discusses an application of Persistence Homology in the field of Symplectic Topology. A major tool in Symplectic Topology are Floer homology groups. These are algebraic invariants that can be associated to pairs of Lagrangian submanifolds. A richer algebraic invariant can be obtained using 
filtered Lagrangian Floer theory. This gives rise to a persistence module and a barcode. Its bar lengths are invariants for the pair of Lagrangians. 
We explain how these numbers can be used to estimate the Lagrangian Hofer distance between the two Lagrangians: It is a well-known stability result  that the bar lengths are lower bounds of the distance. We show how to get an upper bound of the distance in terms of the bar lengths in the special case of equators in a cylinder.

Further Information

Patricia is a Postdoc in Mathematics at ETH Zürich, having recently graduated under the supervision of Prof. Paul Biran.

Patricia is working in the field of symplectic topology. Some key words in her current research project are: Dehn twist, Seidel triangle, real Lefschetz fibrations and Fukaya categories. Besides this, she is a big fan of Hofer's metric, expecially of the Lagrangian Hofer metric and the many interesting open questions related to it. 

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