Lagrangian Intersection Floer Theory

Homological Mirror Symmetry for manifolds of general type

“…For projective manifolds the categories of topological branes are well understood [12,15]. In the simplest setup the category of branes in the B model is identified with the bounded derived category of coherent sheaves D (X ) on a complex manifold X , and the category of A-branes is the derived Fukaya category DFuk(Y ω) of a compact symplectic manifold (Y ω) [11]. It is a triangulated category which is the homotopy category of the category of twisted complexes over the geometrically defined Fukaya category of Lagrangian submanifolds equipped with complex local systems.…”

Exact Lagrangian Submanifolds in T*Sn and the Graded Kronecker Quiver

“…All that we have discussed belongs to the basics of Floer homology theory. Gradings and twisted coefficients were both introduced in [10]; for the use of spin structures see [6]; for the product (1) see [5] (these are by no means the only possible references).…”

A Space of Phylogenetic Networks

“…The rest of this paper is concerned with the relationships among trees, networks, and the real moduli space of curves M 0,n (R), a variety from algebraic geometry [19] appearing in areas such as ζ-motives [13], geometric group theory [6], and Lagrangian Floer theory [11]. There is a substantial relationship between this moduli space and the space of phylogenetic trees: A hint of this relationship was originally discussed in [3], where M 0,n (R) was considered but deemed unsuitable for describing tree space.…”