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Universität Augsburg
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Universität Augsburg
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M. Sc. Elena Isasi Theus
Universitat Politècnica de Catalunya
spricht am
Montag, 6. Juli 2026
um
10:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
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That Hamiltonian Floer theory carries a natural action filtration allows us to produce, in the symplectically aspherical case, persistence modules whose barcodes are stable with respect to Hofer’s metric. Combining this stability theorem with a simple barcode comparison between a small Morse Hamiltonian and the identity gives a barcode-based proof of the nondegeneracy of Hofer’s metric.
This talk will review this proof and the intervening concepts and then focus on what changes in the monotone setting. When $\pi_2(M) eq 0$, the action functional becomes multi-valued, sphere bubbling can occur, and the correct algebraic framework involves Novikov fields, valuations, and Floer-type complexes. Following the work of Usher–Zhang, one obtains verbose and concise barcodes for Floer–Novikov complexes, together with stability results and a chain-level interpretation of boundary depth as the maximal finite bar length. We will explain how these tools suggest a route toward a barcode proof of Hofer nondegeneracy in the monotone case, what is already known, and where the argument still falls short. |
| Hierzu ergeht herzliche Einladung. |
| Emilia Konrad |