Related papers: Newton polygon and string diagram
We outline a program for incorporating holomorphic curves with Lagrangian boundary conditions into symplectic field theory, with an emphasis on ideas, geometric intuition, and a description of the resulting algebraic structures.
Efficient approximation of geodesics is crucial for practical algorithms on manifolds. Here we introduce a class of retractions on submanifolds, induced by a foliation of the ambient manifold. They match the projective retraction to the…
We develop a vertex formalism for topological string amplitudes on ruled surfaces with an arbitrary number of reducible fibers embedded in a Calabi-Yau threefold. Our construction is based on large N duality and localization with respect to…
It is known that graphs cellularly embedded into surfaces are equivalent to ribbon graphs. In this work, we generalize this statement to broader classes of graphs and surfaces. Half-edge graphs extend abstract graphs and are useful in…
We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional N=2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory…
We propose a new family of matrix models whose 1/N expansion captures the all-genus topological string on toric Calabi-Yau threefolds. These matrix models are constructed from the trace class operators appearing in the quantization of the…
We investigate the combinatorial and dynamical properties of so-called nearly Euclidean Thurston maps, or NET maps. These maps are perturbations of many-to-one folding maps of an affine two-sphere to itself. The close relationship between…
We explore \emph{folded} spinning string configurations over torsional Newton Cartan (TNC) geometry with $ R\times S^2 $ topology within the semiclassical approximation. We consider the large $ c $ and/or nonrelativistic (NR) limit…
The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work…
The dynamics of $N\geq 3$ interacting particles is investigated in the non-relativistic context of the Barbour-Bertotti theories. The reduction process on this constrained system yields a Lagrangian in the form of a Riemannian line element.…
In this paper we clarify the relationship between ribbon surfaces of Legendrian graphs and quasipositive diagrams by using certain fence diagrams. As an application, we give an alternative proof of a theorem concerning a relationship…
We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the…
We study the correspondence assigning the vertices of a certain quotient of the local Bruhat-Tits tree for the general linear group over a global function field, to conjugacy classes of maximal orders in some quaternion algebras. The…
We study the superpotentials, quantum parameter space and phase transitions that arise in the study of large N dualities between $\mathcal{N}=1$ SUSY U(N) gauge theories and string models on local Calabi-Yau manifolds. The main tool of our…
Let $X$ be a smooth geometrically connected projective curve over the field of fractions of a discrete valuation ring $R$, and $\mathfrak{m}$ a modulus on $X$, given by a closed subscheme of $X$ which is geometrically reduced. The…
We construct special Lagrangian submanifolds in collapsing Calabi-Yau 3-folds fibered by K3 surfaces. As these 3-folds collapse, the special Lagrangians shrink to 1-dimensional graphs in the base, mirroring the conjectured tropicalization…
Motivated by the algebraic open-closed string models, we introduce and discuss an infinite-dimensional counterpart of the open-closed Hurwitz theory describing branching coverings generated both by the compact oriented surfaces and by the…
We obtain a detailed classification for a class of non-simply connected Calabi-Yau threefolds which are of potential interest for a wide range of problems in string phenomenology. These threefolds arise as quotients of Schoen's Calabi-Yau…
We give a full classification of general affine connections on Galilei manifolds in terms of independently specifiable tensor fields. This generalises the well-known case of (torsional) Galilei connections, i.e. connections compatible with…
The method of topological vertex for topological string theory on toric Calabi-Yau 3-folds is reviewed. Implications of an explicit formula of partition functions in the "on-strip" case, typically the generalized conifolds, are considered.…