Related papers: Multiplicative McKay correspondence in the symplec…

The cobordism ring of symplectic manifolds defined by V.L. Ginzburg is shown to be isomorphic to the Pontrjagin ring of complex-oriented manifolds with free circle actions. This suggests an interpretation of the formal group law of complex…

This is a corrected version of my paper published in Journal of Geometry and Physics 25(1998), 205-226. I added missing cases to the classification theorem 1.1, namely the $SO(n+1)$-manifold $SO(n +2)/ (SO (n) \times SO(2))$, the…

This is the pdf -version of the author's Ph.D. thesis (1995, ULB, Belgium). The notion of symeplectic symmertic space is introduced and studied via Lie theoretical and symplectic geoemetrical methods. The first chapter concerns basic…

We consider the canonical contact structures on links of rational surface singularities with reduced fundamental cycle. These singularities can be characterized by their dual resolution graphs: the graph is a tree, and the weight of each…

Let $G$ be a product of unitary groups and let $(M,\omega)$ be a compact symplectic manifold with Hamiltonian $G$-action. We prove an equivariant formality result for any complex-oriented cohomology theory $\mathbb{E}^*$ (in particular,…

These are lecture notes from my talks at the "Current Developments in Mathematics" conference (Harvard, 2006). They cover a variety of topics involving symplectic cohomology. In particular, a discussion of (algorithmic) classification…

Let G be a finite group acting on a symplectic complex vector space V. Assume that the quotient V/G has a holomorphic symplectic resolution. We prove that G is generated by "symplectic reflectionsd"', i.e. symplectomorphisms with fixed…

We discuss how to use the recent progress in understanding of the $x$-$y$ duality and symplectic duality in the theory of topological recursion and its generalizations in order to efficiently compute the quantum spectral curve operators for…

We establish connections between contact isometry groups of certain contact manifolds and compactly supported symplectomorphism groups of their symplectizations. We apply these results to investigate the space of symplectic embeddings of…

In this note we prove that the symplectic Frobenius Reciprocity established in the paper "Symplectic Induction, Prequantum Induction and Prequantum Multiplicities" as a set bijection is indeed a diffeological diffeomorphism, as conjectured…

Unfortunately, some proofs in the first version of this paper were incorrect. In this revised version, some minor gaps are fixed, one serious mistake found. The main theorem is now claimed only under a restrictive technical assumption. This…

Let $X$ be an oriented 4-manifold which does not have simple SW-type, for example a blow-up of a rational or ruled surface. We show that any two cohomologous and deformation equivalent symplectic forms on $X$ are isotopic. This implies that…

For any toric Calabi-Yau 3-orbifold with transverse A-singularities, we prove Ruan's crepant resolution conjecture and the Gromov-Witten/Donaldson-Thomas correspondence.

We use the techniques of integration of Poisson manifolds into symplectic Lie groupoids to build symplectic resolutions (= desingularizations) of the closure of a symplectic leaf. More generally, we show how Lie groupoids can be used to…

We study the extension of homologically trivial symplectic or Hamiltonian cyclic actions to Hamiltonian circle actions on irrational ruled symplectic $4$-manifolds. On one hand, we construct symplectic involutions on minimal irrational…

A compact real analytic Riemannian manifold M admits a canonical complexification with plurisubharmonic exhaustion function satisfying the homogeneous complex Monge-Ampere equation, called a Grauert tube. From the point of view of complex…

We study the existence of multiple closed Reeb orbits on some contact manifolds by means of $S^1$-equivariant symplectic homology and the index iteration formula. It is proved that a certain class of contact manifolds which admit…

We construct an oriented cobordism between moduli spaces of flat connections on the three holed sphere and disjoint unions of toric varieties, together with a closed two-form which restricts to the symplectic forms on the ends. As…

We observe that numerous symplectic resolutions can be expressed as intersections of twisted cotangent bundles. Additionally, their dual symplectic resolutions can be derived from intersections of dual twisted cotangent bundles. We…

We prove a conjecture by Kreiman and Lakshmibai on a combinatorial description of multiplicities of points on Schubert varieties in Graszmannians in terms of certain sets of reflections in the corresponding Weyl group. The proof is…