I am currently working on bi-invariant metrics on contactomorphism groups with P. Albers and F. Zapolsky, on periodic points of symplectomorphisms, and on various other projects.
Preprints
"The L^p-diameter of the space of contractible loops" (with M. Brandenbursky) - arXiv:2509.07270
"Non-orderability and the contact Hofer norm" (with J. Hedicke), submitted - arXiv:2411.19887
"Weinstein exactness of nearby Lagrangians: towards the Lagrangian C^0 flux conjecture" (with M. Atallah, J.-P. Chassé, R. Leclercq), submitted - arXiv:2410.04158
"A dichotomy for the Hofer growth of area preserving maps on the sphere via symmetrization" (with L. Buhovsky, B. Feuerstein, L. Polterovich), submitted - arXiv:2408.08854
"A counterexample to Lagrangian Poincaré recurrence" (with F. Broćić), submitted - arXiv:2409.14225
"A symplectic Hilbert-Smith conjecture" (with an appendix by L. Polterovich), submitted - arXiv:2403.07195
"Remark on non-contractible closed geodesics and homotopy groups" (with J. Zhang) - arXiv:2307.13877
Accepted/Published
"The chord conjecture for conormal bundles" (with F. Broćić and D. Cant),
Mathematische Annalen, to appear.
"Spectral invariants over the integers" (with Y. Kawamoto),
Advances in Mathematics, 458 (2024) Part B, 109976
"Geometry of symplectic flux and Lagrangian torus fibrations" (with D. Tonkonog, R. Vianna),
Journal of Topology, 17 (2024) no. 4, e70002
"Persistent transcendental Bézout theorems" (with L. Buhovsky, I. Polterovich, L. Polterovich, V. Stojisavljević),
Forum of Mathematics, Sigma, 12 (2024) e72
"Coarse nodal count and topological persistence" (with L. Buhovsky, J. Payette, I. Polterovich, L. Polterovich, V. Stojisavljević),
Journal of the European Mathematical Society, 10.4171/JEMS/1521
"Lagrangian configurations and Hamiltonian maps" (with L. Polterovich) -
Compositio Mathematica, 159 (2023), no.12, 2483 - 2520.
"Symplectic cohomology and a conjecture of Viterbo" -
Geometric and Functional Analysis, 32 (2022), 1514–1543.
"The Schwarz-Milnor lemma for braids and area-preserving diffeomorphisms" (with M. Brandenbursky and M. Marcinkowski)
Selecta Mathematica, 28 (2022), no. 74.
"Hamiltonian no-torsion" (with M. S. Atallah)
Geometry & Topology, 27 (2023), no.7, 2833-2897
"Viterbo conjecture for Zoll symmetric spaces"
Inventiones Mathematicae, 230 (2022), 321–373.
"On the Hofer-Zehnder conjecture"
Annals of Mathematics, 195 (2022), no. 3, 775-839.
"The Z/pZ-equivariant product-isomorphism in fixed point Floer cohomology" (with J. Zhao)
Journal of Symplectic Geometry, 19 (2021), no. 5, 1101--1188.
"Pseudo-rotations and Steenrod squares revisited"
Mathematical Research Letters, 28 (2021), no. 4, 1255–1261.
"Bounds on spectral norms and barcodes" (with A. Kislev)
Geometry & Topology, 25 (2021), no. 7, 3257–3350.
"Lagrangian Shadows and Triangulated Categories" (with P. Biran and O. Cornea)
Astérisque, 426 (2021).
"On the entropy norm on Ham(S^2)" (with M. Brandenbursky)
Annales mathématiques du Québec, 45 (2021), no. 1, 231–237.
"Pseudo-rotations and Steenrod squares" -
Journal of Modern Dynamics, 16 (2020), no. 0, 289–304.
"K-theoretic invariants of Hamiltonian fibrations" (with Y. Savelyev)
Journal of Symplectic Geometry, Vol. 18 (2020), no. 1 , 251--289.
"Persistence modules with operators in Morse and Floer theory" (with L. Polterovich and V. Stojisavljević)
Moscow Mathematical Journal, 17 (2017), no. 4, 757-–786.
"A uniform estimate for general quaternionic Calabi problem (with appendix by Daniel Barlet)" (with S. Alesker)
Advances in Mathematics, 316 (2017), 1--52.
"Lagrangian cobordism and metric invariants" (with O. Cornea)
Journal of Differential Geometry, 112 (2019), no. 1, 1--45
"The L^p-diameter of the group of area-preserving diffeomorphisms of S^2" (with M. Brandenbursky)
Geometry & Topology, 21 (2017), no. 2, 3785--3810.
"On the autonomous norm on the group of Hamiltonian diffeomorphisms of the torus" (with J. Kedra and M. Brandenbursky)
Communications in Contemporary Mathematics, 20 (2018), no. 2, 1750042.
"The Hofer norm of a contactomorphism"
Journal of Symplectic Geometry, 15 (2017), no. 4, 1173 -- 1208.
"On the large-scale geometry of the L^p-metric on the symplectomorphism group of the two-sphere" (with M. Brandenbursky)
Preprints of the IHES M/15/09, arXiv:1304.7037.
"Proof of the main conjecture on g-areas" (with F. Lalonde)
Electronic Research Announcements in Mathematical Sciences (2015), Volume 22, 92-102.
"Autonomous Hamiltonian flows, Hofer's geometry and persistence modules" (with L. Polterovich)
Selecta Mathematica, New Series (2016), Volume 22 , Issue 1, 227-296.
"'Enlacements asymptotiques' revisited"
Annales Mathématiques du Québec (2014), Volume 39, Issue 2, 205-208.
"On the L^p-geometry of autonomous Hamiltonian diffeomorphisms of surfaces" (with M. Brandenbursky)
Mathematical Research Letters (2015), Volume 22, Issue 5, 1275 - 1294.
"The Action homomorphism, quasimorphisms and moment maps on the space of compatible almost complex structures"
Commentarii Mathematici Helvetici (2014), Volume 89, Issue 1, 2014, 69–-123.
"On a uniform estimate for the quaternionic Calabi problem" (with S. Alesker)
Israel Journal of Mathematics (2013), Volume 197, Issue 1, 309--327.
"Remarks on invariants of Hamiltonian loops"
Journal of Topology and Analysis (2010), Volume 2, Issue 3, 277--325.