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Visting Assistant Professor
Symplectic geometry: group actions on manifolds, pseudo-holomorphic curves, and model theory.
In my research, I apply Gromov’s theory of J-holomorphic curves to study group actions on symplectic four-manifolds, thus bridging between “soft” equivariant techniques and the more recent “hard” holomorphic techniques. As a result I get a characterization of Hamiltonian circle and torus actions on symplectic four-manifolds. Recently, I am applying these characterization theorems to study maximal tori and finite subgroups in the group of Hamiltonian symplectomorphisms, and the equivariant cohomology, for four-manifolds and for Hamiltonian complexity one spaces.
I am also interested in applying model theory to study almost complex manifolds, and in the structures of moduli spaces of J-holomorphic curves.
- Circle actions on symplectic four-manifolds (with T.S. Holm and Apendix by Tair Pnini), arXiv:1507.05972v3, Communications in Analysis and Geometry (to appear).
- Distinguishing symplectic blowups of the complex projective plane (with Y. Karshon), arXiv:1407.5312v1, Journal of Symplectic Geometry (to appear).
- Symplectic geometry on moduli spaces of J-holomorphic curves (with J. Coffey and A. Pelayo) Annals of Global Analysis and Geometry 41 (2012), no. 3, 265-280.
- Holomorphic shadows in the eyes of model theory, Transactions of the AMS 363 (2011), no. 6, 3287-3307.
- A compact symplectic four- manifold admits only finitely many inequivalent toric actions (with Y. Karshon and M. Pinsonnault), Journal of Symplectic Geometry 5 (2007), no. 2, 139-166.
- Circle and torus actions on equal symplectic blow-ups of CP2 (with Y. Karshon), Mathematical Research Letters 14 (2007), no. 5, 807- 823.