Related papers: The closed-open string map for $S^1$-invariant Lag…

We construct, for a homogeneous Lagrangian of arbitrary order in two independent variables, a differential 2-form with the property that it is closed precisely when the Lagrangian is null. This is similar to the property of the `fundamental…

We present detailed discussions on the stochastic Hamiltonians for non-critical string field theories on the basis of matrix models. Beginning from the simplest $c=0$ case, we derive the explicit forms of the Hamiltonians for the higher…

We investigate the question of whether the spectral metric on the orbit space of a fiber in the disk cotangent bundle of a closed manifold, under the action of the compactly supported Hamiltonian diffeomorphism group, is bounded. We utilize…

We consider a class of conformal models describing closed strings in axially symmetric stationary magnetic flux tube backgrounds. These models are closed string analogs of the Landau model of a particle in a magnetic field or the model of…

We develop an equivariant Lagrangian Floer theory for Liouville sectors that have symmetry of a Lie group $G$. Moreover, for Liouville manifolds with $G$-symmetry, we develop a correspondence theory to relate the equivariant Lagrangian…

We conjecture the existence of a `compactified' version of Fukaya's homology for symplectic manifolds, which carries a canonical 2-Gerstenhaber algebra structure. This may help to understand the 2-Lie algebra structure involved in models…

We study the singularities of closures of Iwahori orbits on loop spaces of symmetric varieties extending the celebrated work of Lusztig-Vogan to the affine setting. We show that the IC-complexes of orbit closures (with possible non-trivial…

In an earlier paper, we showed that the moduli space of deformations of a smooth, compact, orientable special Lagrangian submanifold L in a symplectic manifold X with a non-integrable almost complex structure is a smooth manifold of…

We describe the (bigraded) Hochschild cohomology of graded gentle algebras along with the Gerstenhaber bracket and cup product. In particular, this yields a description of the Hochschild cohomology of partially wrapped Fukaya categories of…

We show that the (torsional) nonrelativistic string sigma models on $ R\times S^2 $ can be mapped into \emph{deformed} Rosochatius like integrable models in one dimension. We also explore the associated Hamiltonian constrained structure by…

In this paper we study a cohomology theory of compatible Leibniz algebra. We construct a graded Lie algebra whose Maurer-Cartan elements characterize the structure of compatible Leibniz algebras. Using this, we study cohomology,…

We introduce the notion of cyclic cohomology of an A-infinity algebra and show that the deformations of an A-infinity algebra which preserve an invariant inner product are classified by this cohomology. We use this result to construct some…

In this short note we discuss high-dimensional examples of Legendrian submanifolds of the standard contact Euclidean space with an infinite number of exact Lagrangian fillings up to Hamiltonian isotopy. They are obtained from the examples…

Configuration space integrals have in recent years been used for studying the cohomology of spaces of (string) knots and links in $\mathbb{R}^n$ for $n>3$ since they provide a map from a certain differential algebra of diagrams to the…

Let G be a compact Lie group. By work of Chataur and Menichi, the homology of the space of free loops in the classifying space of G is known to be the value on the circle in a homological conformal field theory. This means in particular…

We study a special sort of 2-dimensional extended Topological Quantum Field Theories (TQFTs) which we call open-closed TQFTs. These are defined on open-closed cobordisms by which we mean smooth compact oriented 2-manifolds with corners that…

We study collections of exact Lagrangian submanifolds respecting some uniform Riemannian bounds, which we equip with a metric naturally arising in symplectic topology (e.g. the Lagrangian Hofer metric or the spectral metric). We exhibit…

In this paper, which is a natural continuation of our previous paper math.DG/0504557, we describe some special Lagrangians of cohomogeneity one in the resolved conifold. Our main result gives a foliation of the resolved conifold by…

We show that string algebras are `homologically tame' in the following sense: First, the syzygies of arbitrary representations of a finite dimensional string algebra $\Lambda$ are direct sums of cyclic representations, and the left…

We study the equivariant generalization of topological strings on toric manifolds, focusing in particular on defining the contributions of constant maps in the genus expansion of the partition function. This approach regularizes the…