email: yasha.savelyev@gmail.com
Quantum characteristic classes and the Hofer metric, Geometry & Topology 12, 2277–2326, (2008)
(This is a slightly condensed version of my thesis work.)
Virtual Morse theory on ΩHam(M, ω), J. Differ. Geom. 84, No. 2, 409-425, (2010)
Bott periodicity and stable quantum classes, Selecta Math. N.S., 2012, Volume 19, Issue 2, 439-460, (2013)
Gromov K-area and jumping curves in CPn, Alg. and Geom. Topology, 12, 2317-2327, (2012)
Proof of the index conjecture in Hofer geometry, Math. Res. Lett, Vol 20, 981-984, (2013)
Morse theory for the Hofer length functional, Journ. of Topology and Analysis, 6:2, (2014)
On the injectivity radius in Hofer geometry, (Joint with Francois Lalonde), Electronic Research Announcements, Vol 21, 177-185, (2014)
Yang-Mills theory and jumping curves, Inter. J. Math., 26:5, 13 pgs, (2015)
On the Hofer geometry injectivity radius conjecture, International Mathematics Research Notices, 7253-7267, (2016); doi: 10.1093/imrn/rnw023
Floer theory and topology of Diff(S2), Journal of Symplectic Geometry, Vol. 15, No. 3, pg. 853-859, (2017) DOI: http://dx.doi.org/10.4310/JSG.2017.v15.n3.a8
(Note the title change, previously: “Volume preserving …”)
Extended Fuller index, sky catastrophes and the Seifert conjecture, Inter. J. Math., (2018), pg. 1-22, https://doi.org/10.1142/S0129167X18500969
Author note: There is a very interesting conjecture here on non-existence of sky catastrophes for Reeb vector fields, and for which I welcome aid.
Mean curvature versus diameter and energy quantization, Annales mathematiques du Quebec, (2019), 1-7, (2019), 10.1007/s40316-019-00127-0
K-theoretic invariants of Hamiltonian fibrations, (with Egor Shelukhin), Journal of Symplectic Geometry, Vol. 18, No. 1 (2020), pg. 251-289.
This introduces some new K-theoretic quantization techniques for Hamiltonian fibrations, and uses this to deduce some new results on topology of Ham(CPn).
Global Fukaya category I, International Mathematics Research Notices, https://doi.org/10.1093/imrn/rnad013, (2023), 85 pages
In particular this contains a proof of one strong sense of a conjecture of Teleman on existence of continuous action of the group of Hamiltonian symplectomorphisms on the Fukaya category of a symplectic manifold.
Locally conformally symplectic deformation of Gromov non-squeezing, Arch. Math. https://doi.org/10.1007/s00013-023-01922-6 (2023)
Pseudoholomorphic curves on the lcs-fication of contact manifolds (With Yong-Geun Oh), Adv. Geom. 23, No. 2, 153-190 (2023)
A remark on deformation of Gromov non-squeezing, Differential geometry and its applications, https://www.sciencedirect.com/science/article/pii/S0926224525000373?dgcid=author, (2025), 5 pages
Smooth simplicial sets and universal Chern-Weil for infinite dimensional groups, J. London Math. Soc., 113, No. 1, 1-65 (2026)
Strict contactomorphisms are scarce (With Yong-Geun Oh)
On the space of metrics with non-positive curvature, 5 pages
Global Fukaya category II, 32 pages
Elliptic curves in lcs manifolds and metric invariants, 34 pages
Incompleteness theorems via Turing category, 20 pages
Geodesic string counting invariants of manifolds, 18 pages
Hamiltonian elements in algebraic K-theory, 13 pages
Quantum Maslov classes, 25 pages
Simultaneous Go via quantum collapse, 20 pages
Spectral geometry of the group of Hamiltonian symplectomorphisms