Related papers: Classification of Lagrangian Fibrations over a Kle…

We show that braidings on a fusion category $\mathcal{C}$ correspond to certain fusion subcategories of the center of $\mathcal{C}$ transversal to the canonical Lagrangian algebra. This allows to classify braidings on non-degenerate and…

By summarizing and extending the Lagrangian densities of the general relativity and the Kibble's gauge theory of gravitation,a further generalized Lagrangian density for a gravitational system is obtained and analyzed in greater detail,…

This paper continues the study initiated in [ISZ25] on the moduli of surfaces admitting lc-trivial fibrations. Using the techniques developed in [ISZ25], we (1) provide a classification of the surfaces appearing on the boundary of the…

We present an explicit construction of the basic bundle gerbes with connection over all connected compact simple Lie groups. These are geometric objects that appear naturally in the Lagrangian approach to the WZW conformal field theories.…

We introduce a topological variant of the Grothendieck construction which serves to represent every fiber bundle over an Alexandroff space. Using this result we give a classification theorem for fiber bundles over Alexandroff spaces with…

We study the monodromy representations underlying compact Lagrangian fibrations. In the case where the associated period map is generically immersive, we prove that the mondromy representation is irreducible over $\mathbb{C}$. In the…

Let $K$ be a number field, and let $\mathcal{X}$ be a proper regular flat scheme over $\mathcal{O}_{K}$ with a generic fiber $X$ geometrically connected over $K$. We prove that there is an exact sequence up to finite groups $0\rightarrow…

In this paper we introduce a new way of displacing Lagrangian fibers in toric symplectic manifolds, a generalization of McDuff's original method of probes. Extended probes are formed by deflecting one probe by another auxiliary probe. Using…

In this note, we first introduce a boundary problem for Lagrangian submanifolds, analogous to the problem for free boundary hypersurfaces and capillary hypersurfaces. Then we present several interesting examples of Lagrangian submanifolds…

We observe that general reducible curves in sufficiently positive linear systems on K3 surfaces are of a form that generalises Kodaira's classification of singular elliptic fibres and thus call them extended ADE curves. On such a curve $C$,…

We use Luttinger surgery to show that there are no Lagrangian Klein bottles in $S^2\times S^2$ in the $\mathbb{Z}_2$-homology class of an $S^2$-factor if the symplectic area of that factor is at least twice that of the other.

We study how regularity along a submanifold of a differential or microdifferential system can propagate from a family of submanifolds to another. The first result is that a microdifferential system regular along a lagrangian foliation is…

Lagrangian multiforms provide a variational framework for describing integrable hierarchies. This thesis presents two approaches for systematically constructing Lagrangian one-forms, which cover the case of finite-dimensional integrable…

Let $X\to\P^n$ be an irreducible holomorphic symplectic manifold of dimension $2n$ fibred over $\P^n$. Matsushita proved that the generic fibre is a holomorphic Lagrangian abelian variety. In this article we study the discriminant locus…

This (partially expository) paper discusses Lagrangian Floer cohomology in the context of Lefschetz fibrations, with emphasis on the algebraic structures encountered there. In addition to the well-known directed A_infinity algebras which…

In this note, we show that if $f\colon M\rightarrow X$ is a germ of a projective Lagrangian fibration from a holomorphic symplectic manifold $M$ onto a normal analytic variety $X$ with isolated quotient singularities, then $X$ is smooth. In…

Let \Sigma be a complete minimal Lagrangian submanifold of \C^n. We identify regions in the Grassmannian of Lagrangian subspaces so that whenever the image of the Gauss map of \Sigma lies in one of these regions, then \Sigma is an affine…

We use the ultrafilter-convergence axiomatics for topological spaces to motivate in detail a gentle categorical introduction, first to Barr's Set-based relational T-algebras, and then to Burroni's T-preorders internal to a category C, here…

This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such…

We establish a general normal subgroup theorem for commensurators of lattices in locally compact groups. While the statement is completely elementary, its proof, which rests on the original strategy of Margulis in the case of higher rank…