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), pp. 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, 85 pages, International Mathematics Research Notices, https://doi.org/10.1093/imrn/rnad013, (2023)
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.
Pseudoholomorphic curves on the lcs-fication of contact manifolds (With Yong-Geun Oh), Adv. Geom. 23, No. 2, 153-190 (2023)
Locally conformally symplectic deformation of Gromov non-squeezing, Arch. Math. https://doi.org/10.1007/s00013-023-01922-6 (2023)
A remark on deformation of Gromov non-squeezing, 5 pages, Differential geometry and its applications, https://www.sciencedirect.com/science/article/pii/S0926224525000373?dgcid=author, (2025)
Strict contactomorphisms are scarce (With Yong-Geun Oh)
Smooth simplicial sets and universal Chern-Weil for infinite dimensional groups, 56 pages
On the space of metrics with non-positive curvature, 5 pages
Global Fukaya category II: applications, 28 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, 11 pages
Quantum Maslov classes, 25 pages
Simultaneous Go via quantum collapse, 11 pages
Spectral geometry of the group of Hamiltonian symplectomorphisms