Related papers: Almost Lagrangian Obstruction
We give a construction of Lagrangian torus fibrations with controlled discriminant locus on certain affine varieties. In particular, we apply our construction in the following ways. We find a Lagrangian torus fibration on the 3-fold…
Two main themes populate this Thesis's pages: transgression forms as Lagrangians for gauge theories and the Abelian semigroup expansion of Lie algebras. A transgression form is a function of two gauge connections whose main property is its…
Let k>2. We prove that the cotangent bundles of oriented homotopy (2k-1)-spheres S and S' are symplectomorphic only if the classes defined by S and S' agree up to sign in the quotient group of oriented homotopy spheres modulo those which…
In the usual setup, the grading on Floer homology is relative: it is unique only up to adding a constant. "Graded Lagrangian submanifolds" are Lagrangian submanifolds with a bit of extra structure, which fixes the ambiguity in the grading.…
We study Lagrangian subalgebras of a semisimple Lie algebra with respect to the imaginary part of the Killing form. We show that the variety $\Lagr$ of Lagrangian subalgebras carries a natural Poisson structure $\Pi$. We determine the…
Necessary optimality conditions in Lagrangian form and the sequential minimization framework are extended to mixed-integer nonlinear optimization, without any convexity assumptions. Building upon a recently developed notion of local…
We provide a prorepresenting object for the noncommutative derived deformation problem of deforming a module $X$ over a differential graded algebra. Roughly, we show that the corresponding deformation functor is homotopy prorepresented by…
We investigate deformations of lagrangian manifolds with singularities. We introduce a complex similar to the de Rham-complex whose cohomology calculates deformation spaces. Examples of singular lagrangian varieties are presented and…
We study a class of weakly coupled Hamilton-Jacobi systems with a specific aim to perform a qualitative analysis in the spirit of weak KAM theory. Our main achievement is the definition of a family of related action functionals containing…
The main theme of this paper is the Thomas-Yau conjecture, primarily in the setting of exact, (quantitatively) almost calibrated, unobstructed Lagrangian branes inside Calabi-Yau Stein manifolds. In our interpretation, the conjecture is…
Given a Lagrangian fibration, we provide a natural construction of a mirror Landau-Ginzburg model consisting of a rigid analytic space, a superpotential function, and a dual fibration based on Fukaya's family Floer theory. The mirror in the…
This is a continuation of part I in the series of the papers on Lagrangian Floer theory on toric manifolds. Using the deformations of Floer cohomology by the ambient cycles, which we call bulk deformations, we find a continuum of…
This note presents basic restrictions on the topology "general" Lagrangian surfaces of hyper-K\"ahler $4$-folds and a remark on the interaction of a Lagrangian subvariety with a Lagrangian fibration of the associated hyper-K\"ahler variety.
Let $P \subset \mathbb{R}^m$ be a polytope of dimension $m$ with $n$ facets. Assume that $P$ is Delzant and Fano. We associate a monotone embedded Lagrangian $L \subset \mathbb{C}P^{n-1}$ to $P$. As an abstract manifold, the Lagrangian $L$…
This paper is devoted to the study of a certain class of principal bundles on del Pezzo surfaces, which were introduced and studied by Friedman and Morgan in \cite{FMdP}: The two authors showed that there exists a unique principal bundle…
We show that the cardinality of the transverse intersection of two compact exact Lagrangian submanifolds in a cotangent bundle is bounded from below by the dimension of the Hom space of sheaf quantizations of the Lagrangians in Tamarkin's…
Consider a Stein manifold M obtained by plumbing cotangent bundles of manifolds of dimension greater than or equal to 3 at points. We prove that the Fukaya category of closed exact Lagrangians with vanishing Maslov class in M is generated…
The Bialynicki-Birula decomposition of the space of lambda-connections restricts to the Morse stratification on the moduli space of Higgs bundles and to the partial oper stratification on the de Rham moduli space of holomorphic connections.…
Consider a Maslov zero Lagrangian submanifold diffeomorphic to a Lie group on which an anti-symplectic involution acts by the inverse map of the group. We show that the Fukaya $A_\infty$ endomorphism algebra of such a Lagrangian is…
Using Quillen-Lurie deformation theory formalism we develop an obstruction theory for studying the stable $\infty$-category of modules over a given geometric $\infty$-stack. The obstruction theory studies the problem of lifting compact…