Publications

I am currently working on bi-invariant metrics on contactomorphism groups with P. Albers and F. Zapolsky, on periodic points of symplectomorphisms, and on other projects.

Preprints

• "The chord conjecture for conormal bundles" (with F. Broćić and D. Cant), submitted - arXiv:2401.08842

• "Spectral invariants over the integers" (with Y. Kawamoto), submitted - arXiv:2310.19033

• "Remark on non-contractible closed geodesics and homotopy groups" (with J. Zhang), submitted - arXiv:2307.13877

• "Geometry of symplectic flux and Lagrangian torus fibrations" (with D. Tonkonog, R. Vianna), submitted - arXiv:1804.02044

Accepted/Published

• "Persistent transcendental Bézout theorems" (with L. Buhovsky, I. Polterovich, L. Polterovich, V. Stojisavljević), 
  Forum of Mathematics Sigma, accepted; preprint available at arXiv:2307.02937 

• "Coarse nodal count and topological persistence" (with L. Buhovsky, J. Payette, I. Polterovich, L. Polterovich, V. Stojisavljević),
  Journal of the European Mathematical Society, accepted; preprint available at arXiv:2206.06347 

• "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.