Category Archives: Uncategorized

The ABHS construction of contact forms with high systolic ratio

  The purpose of this post, which accompanies a student seminar talk, is to explain a construction of Abbondandolo-Bramham-Hryniewicz-Salomão of contact forms with high systolic ratio. To review what this means, let be a compact domain in with smooth boundary … Continue reading

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Two or infinitely many Reeb orbits

Sorry this blog has been quiet for a while. There are a lot of things I would like to write about, but I have been trying to finish some papers. In particular, Dan Cristofaro-Gardiner, Dan Pomerleano, and I recently completed … Continue reading

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Version 2 of “Beyond ECH capacities”

I just posted a revised version of the preprint “Beyond ECH capacities” to the arXiv. It should appear on Monday, but you can view it here first. The new version corrects some embarrassing/horrifying typos, clarifies a few things, and includes … Continue reading

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Comparison with Ekeland-Hofer

Helmut Hofer asked me how the symplectic embedding obstructions in “Beyond ECH capacities” compare to the obstructions given by Ekeland-Hofer capacities, for symplectic embeddings between ellipsoids and polydisks. I happened to know the answer to this, using something which I … Continue reading

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Beyond ECH capacities

In case the last couple of postings were confusing, I have now posted a preprint explaining the story. Here is the abstract: “ECH (embedded contact homology) capacities give obstructions to symplectically embedding one four-dimensional symplectic manifold with boundary into another. … Continue reading

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Symplectic embeddings of polydisks into polydisks

If I am not mistaken, the methods in the previous post (plus a conjecture about the ECH chain complex of perturbed boundaries of convex toric domains) can be used to show that if are real numbers with and , and … Continue reading

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Hind-Lisi and more

References for this post: [HL] R. Hind and S. Lisi, Symplectic embeddings of polydisks [CONCAVE] K. Choi, D. Cristofaro-Gardiner, D. Frenkel, M. Hutchings, and V. Ramos, Symplectic embeddings into four-dimensional concave toric domains [T3] M. Hutchings and M. Sullivan, Rounding … Continue reading

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