20 citations · 34 across the 8 of their papers we have counts for
8 papers
Pseudotropical curves
Sergei Lanzat, Michael Polyak
We propose a generalization of tropical curves by dropping the rationality and integrality requirements while preserving the balancing condition. An interpretation of such curves a…
On the contact mapping class group of the contactization of the - Milnor fiber
Sergei Lanzat, Frol Zapolsky
We construct an embedding of the full braid group on strands , , into the contact mapping class group of the contactization of the -Mil…
Counting isotropic tangent lines of hypersurfaces
Sergei Lanzat
Consider the standard symplectic $(\RR^{2n}, ω_0)$, a point $p\in\RR^{2n}$ and an immersed closed orientable hypersurface $Σ\subset\RR^{2n}\minus\{p\}$, all in general position. We…
Quantum homology of compact convex symplectic manifolds
Sergei Lanzat
We study the space of pseudo-holomorphic spheres in compact symplectic manifolds with convex boundary. We show that the theory of Gromov-Witten invariants can be extended to the cl…
Hamiltonian Floer homology for compact convex symplectic manifolds
Sergei Lanzat
We construct absolute and relative versions of Hamiltonian Floer homology algebras for strongly semi-positive compact symplectic manifolds with convex boundary, where the ring stru…
Quasi-morphisms and symplectic quasi-states for convex symplectic manifolds
Sergei Lanzat
We use quantum and Floer homology to construct (partial) quasi-morphisms on the universal cover of the group of compactly supported Hamiltonian diffeomorphisms for a certain class…
Integrating curvature: from Umlaufsatz to J^+ invariant
Sergei Lanzat, Michael Polyak
Hopf's Umlaufsatz relates the total curvature of a closed immersed plane curve to its rotation number. While the curvature of a curve changes under local deformations, its integral…
Counting real curves with passage/tangency conditions
Sergei Lanzat, Michael Polyak
We study the following question: given a set P of 3d-2 points and an immersed curve G in the real plane R^2, all in general position, how many real rational plane curves of degree…