# Research

Here is a list of my papers, with some relevant links.

Preprints:

A global Le Calvez-Yoccoz property of area-preserving surface diffeomorphisms and three-dimensional Reeb flows [with R. Prasad]

On the large-scale geometry of domains in an exact symplectic four-manifold [with R. Hind]

Proof of Hofer-Wysocki-Zehnder's two or infinity conjecture [with U. Hryniewicz, M. Hutchings and H. Liu]

Video available here

Another video available here (with a few more details)

Slides available here

On the agreement of symplectic capacities in high dimension [with R. Hind]

Boundaries of open symplectic manifolds and the failure of packing stability [with R. Hind]

The smooth closing lemma for area-preserving surface diffeomorphisms [with R. Prasad and B. Zhang]

Subleading asymptotics of link spectral invariants and homeomorphism groups of surfaces [with V. Humiliere, C. Y. Mak, S. Seyfaddini, and I. Smith]

[Generic higher asymptotics of holomorphic curves and applications [with M. Hutchings and B. Zhang] 6/30/19 Draft available here: Higher asymptotics draft

Papers that have been published or accepted for publication:

On infinite staircases in toric symplectic 4-manifolds [with T. Holm, A. Mandini, and A. Pires], J. Diff. Geom, to appear

Video available here

Contact three-manifolds with exactly two simple Reeb orbits [with U. Hryniewicz, M. Hutchings and H. Liu], Geom. Topol., to appear

A note on the existence of U-cyclic elements in periodic Floer homology [with D. Pomerleano, R. Prasad and B. Zhang], Proc. AMS (Series B: open access), to appear

PFH spectral invariants on the two-sphere and the large scale geometry of Hofer’s metric [with V. Humiliere and S. Seyfaddini], J. Eur. Mat. Soc. (JEMS), to appear:

Video available here

Proof of the simplicity conjecture [with V. Humiliere and S. Seyfaddini], Ann. Math., to appear:

Video available here

A Bourbaki seminar by E. Ghys (see also the JEMS article): notes, video.

An NSF highlights article: article

Quantitative Heegaard Floer cohomology and the Calabi invariant [with V. Humiliere, C. Y. Mak, S. Seyfaddini, and I. Smith], Forum of Math., Pi, Volume 10 (2022):

Video available here

Special eccentricities of rational four-dimensional ellipsoids Alg. Geom. Top. 22.5 (2022)

Higher symplectic capacities and the stabilized embedding problem for integral ellipsoids [with R. Hind and K. Siegel], Journ. Fixed Point Theory and App., special issue in honor of Claude Viterbo (2022)

Sub-leading asymptotics of ECH capacities [with N. Savale], Selecta Math. 65 (2020).

The action spectrum characterizes closed contact 3-manifolds all of whose Reeb orbits are closed [with M. Mazzucchelli], Comm. Math. Helv. 95 (2020):

Oberwolfach report

Ehrhart polynomials and symplectic embeddings of ellipsoids [with A. Kleinman] Jour. Lon. Math. Soc. (2020)

Symplectic embeddings from concave toric domains into convex ones, J. Diff. Geom. 112 (2019), 199-232:

Video

New examples of period collapse [with T. Li and R. Stanley], Disc. and Comp. Geo. 61(2), 227-246 (2019):

Video

Torsion contact forms in three dimensions have two or infinitely many Reeb orbits [with M. Hutchings and D. Pomerleano], Geom. Topol. 23 (2019):

Video

Symplectic embeddings of products [with R. Hind], Comm. Math. Helv., 93 (2018), 1-32:

Video

The ghost stairs stabilize to sharp symplectic embedding obstructions [with R. Hind and D. McDuff], Journ. of Top. 11.2 (2018), 309-378.

Symplectic embeddings of four-dimensional ellipsoids into integral polydiscs [with D. Frenkel and F. Schlenk], Alg. Geom. Top. 17 (2017), 1189-1260.

From one Reeb orbit to two [with M. Hutchings], Journ. of Diff. Geom. 102.1 (2016), 25-36.

The asymptotics of ECH capacities [with M. Hutchings and V. Ramos], Invent. Math. 199.1 (2015), 187-214.

Oberwolfach report

Video

A Bourbaki seminar by V. Humiliere on work of Asaoka-Irie discusses this result: notes

Symplectic embeddings into four-dimensional concave toric domains [with K. Choi, D. Frenkel, M. Hutchings, and V. Ramos], Journ. of Top. 7.4 (2014), 1054-1076.

The absolute gradings on embedded contact homology and Seiberg-Witten Floer cohomology, Alg. and Geom. Topol. 13 (2013), 2239-2260.