Decomposes moduli space of Riemann surfaces into convex polytopes.
problem Decomposing moduli space of Riemann surfaces into cells.
method Using Nakamura graphs to define cell decomposition, parametrized by graphs or permutations.
result Cells are convex polytopes defined by light-cone string parameters.
We construct a cut-off version of nonpertubative closed Bosonic string field theory in the light-cone gauge with imaginary string coupling constant. We show that the partition function is a continuous function of the string coupling constant, and conjecture a relation between the formal power series expansion of this p…
The paper connects curves on a light cone to KdV equations.
problem Understanding differential invariants of curves on a light cone.
method Poisson equivalence and centro-affine action of Lorentzian group.
result Solutions of KdV equations as flows of curves on the cone.
Curvature flow and inverse curvature flow solutions on 2D light cone identified.
problem Identifying self-similar solutions to curvature flow and inverse curvature flow on 2D light cone.
method Proved correspondence between CF and ICF solutions, analyzed ellipses and hyperboles, and characterized self-similar solutions.
result Ellipses and hyperboles are the only curves evolving under homotheties on the 2D light cone.
Classifies surfaces with zero mean curvature in a light cone.
problem Classifying surfaces with zero mean curvature in a light cone.
method Examined geodesics and screw motions, used Weierstrass representations.
result Complete classification of ruled zero mean curvature surfaces.
Solves surface problem in 3D light cone.
problem Björling problem for zero mean curvature surfaces in the three-dimensional light cone.
method Solves the Björling problem for zero mean curvature surfaces in the three-dimensional light cone.
result Constructs and classifies all rotational zero mean curvature surfaces.
This paper mainly aims to establish the well-posedness on time interval [ 0 , ε − 1 2 T ] [0,\varepsilon^{-\frac{1}{2}}T] [ 0 , ε − 2 1 T ] of the classical initial problem for the bosonic membrane in the light cone gauge. Here ε \varepsilon ε is the small parameter measures the nonlinear effects. In geometric, the bosonic membrane are timelike submanifo…
The paper studies hypersurface evolution in a light-cone and curvature flow.
problem Investigating the evolution of hypersurfaces in a light-cone.
method Exploring variational problems associated with hypersurfaces and curvature flow.
result Established perpetual existence and smooth convergence of curvature flow to a circle.
Paper proves rigidity of certain manifold immersions into specific spacetimes.
problem Rigidity of isometric immersions into light cones.
method Analyzes Riemannian manifolds of dimension n-1 into light cones of n+1 spacetimes.
result Shows rigidity of isometric immersions for n ≥ 3.
New inequality shows all special submanifolds in light cone are totally umbilical spheres.
problem Characterizing submanifolds with parallel mean curvature in Lorentz-Minkowski spacetime.
method Established an integral inequality and used it to derive a rigidity result.
result All compact submanifolds with parallel mean curvature in light cone are totally umbilical spheres.
The paper studies volumes of conformally flat manifolds in light-cone geometry.
problem Volume maximization of conformally flat manifolds in light-cone geometry.
method Computes variational formulas for the volume of hypersurfaces in light-cone.
result Hypersurfaces of conformally flat manifolds maximize volume in certain null hypersurfaces.
New algorithms predict spatio-temporal data without assuming its structure.
problem Predicting high-dimensional spatio-temporal data without assuming its structure.
method Light cone decompositions and three simple algorithms for predictive state reconstruction.
result Good predictive performance and distributions over spatio-temporal data.
Extends gauge conditions for superparticle to conic neighbourhood.
problem Applying gauge conditions to superparticle in momentum space.
method Patching gauge conditions over different parts of field space.
result Extension of light-cone gauge to conic neighbourhood.
The study proves that certain constant mean curvature surfaces in a specific cone are either spheres or horospheres.
problem Characterizing constant mean curvature surfaces in a three-dimensional light cone.
method Analyzing entire constant mean curvature graphs in the light cone Q + 3 \mathbb{Q}^3_+ Q + 3 under the condition of bounded Gaussian curvature. result Entire constant mean curvature graphs in the light cone are either horospheres or spheres.
The paper classifies periodic solitons in curve flows on the light-cone.
problem Investigating periodic solitons in curve flows on the light-cone.
method Deriving Harnack inequality for heat flow, classifying space-periodic solitons for a third-order curvature flow.
result Closed soliton solutions form a family of transcendental curves with specific rotation indices.
Complex geometry and symplectic geometry are mirrors in string theory. The recently developed generalised complex geometry interpolates between the two of them. On the other hand, the classical and quantum mechanics of a finite number of degrees of freedom are respectively described by a symplectic structure and a comp…
Reconstructing manifold structure from boundary light observations.
problem Reconstructing Lorentzian manifold structure from boundary light observations.
method Constructive proof using Snell's law for reflections at the boundary.
result Topological, differentiable, and conformal structure of subsets of sources uniquely determined.
Proves compatibility of light cones and projective structures.
problem Clarifying different concepts of compatibility between conformal and projective structures.
method Analyzes compatibility criteria introduced by Ehlers-Pirani-Schild and Trautman-Scholz.
result Proves that the compatibility criterion introduced by Ehlers-Pirani-Schild is correct.
The paper classifies orbits of S O ( 3 , 1 ) SO(3,1) S O ( 3 , 1 ) in a 4D Minkowski space.
problem Classifying orbits of S O ( 3 , 1 ) SO(3,1) S O ( 3 , 1 ) in a 4D Minkowski space. method Analyzing the stabilizer and r-slice of L ( ⋀ 2 E 1 4 ) L(\bigwedge^2 E^4_1 ) L ( ⋀ 2 E 1 4 ) . result Each S O ( 3 , 1 ) SO(3,1) S O ( 3 , 1 ) -orbit in L ( ⋀ 2 E 1 4 ) L(\bigwedge^2 E^4_1 ) L ( ⋀ 2 E 1 4 ) is either a neutral hypersurface homothetic to L ± \mathcal{L}_{\pm} L ± or a hypersurface with a two-dimensional involutive distribution. Novel prediction method using string invariants with evolutionary optimization.
problem Optimal prediction parameters for string invariants.
method Evolutionary algorithm for parameter optimization.
result Method performs well in single step prediction but needs improvement for multiple steps.
Measuring supernova neutrinos removes spacetime's conformal freedom.
problem Determining the conformal factor of spacetime's visible part.
method Measuring neutrino cones in addition to light cones.
result The conformal factor can now be determined.
This paper constructs an explicit {e}-structure for certain 2-nondegenerate hypersurfaces.
problem Characterizing and classifying 2-nondegenerate Levi rank 1 hypersurfaces in complex space.
method Normalization of group parameters and construction of an explicit {e}-structure.
result An explicit {e}-structure is constructed for hypersurfaces where primary invariants do not vanish.
New tools identify potential counter-examples to string theory conjectures.
problem Classical de Sitter solutions with specific conditions.
method Developed new tools and constraints to explore parameter space.
result Identified corners of parameter space where counter-examples could be found.
Study submanifolds in null hypersurfaces of generalized Robertson-Walker spacetimes.
problem Characterize submanifolds in null hypersurfaces of generalized Robertson-Walker spacetimes.
method Analyze light cones, lightlike cylinders, and null cones in specific spacetimes; provide conditions for conformal diffeomorphism.
result Conditions guaranteeing conformal diffeomorphism to hyperbolic space, round cylinder, and sphere.
Existence and uniqueness in R n , 1 {\Bbb R}^{n,1} R n , 1 of entire spacelike hypersurfaces contained in the future of the origin O O O and asymptotic to the light-cone, with scalar curvature prescribed at their generic point M M M as a negative function of the unit vector O m → \overrightarrow{Om} O m pointing in the direction of $\overrighta…
The paper shows bounds for a geometric flow related to Type IIB string theory.
problem Establishing derivative bounds for a geometric flow in non-Kähler geometry.
method Unified formulation of the flow with Ricci flow, proving bounds from metric and torsion 1-form uniform bounds.
result Derivative bounds follow from uniform metric and torsion 1-form bounds.
STANCE learns string similarity using optimal transport alignment.
problem Computing similarity between strings for record linkage and entity resolution.
method Character encoding, optimal transport alignment, convolutional neural network scoring.
result STANCE outperforms state-of-the-art models on alias detection datasets.
String geometry theory uniquely determines classical action with T-symmetry.
problem Non-renormalizability and loop corrections in string theory.
method Distinguishes effects of β and ħ parameters, proving no loop corrections.
result No loop corrections in string geometry theory, avoiding non-renormalizability.
The paper establishes a correspondence between special Kähler manifolds and their deformations.
problem Mapping between affine and projective special Kähler manifolds.
method Formulation of a correspondence and application to r-maps in string theory.
result One-parameter deformations of projective special Kähler manifolds correspond to perturbative α'-corrections.
We construct and study a family of double-periodic almost entire solutions of the maximal surface equation. The solutions are parameterized by a submanifold of 3 × 3 3\times 3 3 × 3 -matrices (the so-called generating matrices). We show that the constructed solutions are either space-like or of mixed type with the light-cone type…
In a given 4d spacetime bakcground, one can often construct not one but a family of distinct N=2 string theories. This is due to the multiple ways N=2 superconformal algebra can be embedded in a given worldsheet theory. We formulate the principle of obtaining different physical theories by gauging different embeddings …
New mappings in Minkowski spacetime classified under mild conditions.
problem Characterizing mappings in Minkowski spacetime.
method Analyzing mappings under minimal assumptions.
result Mappings fall into three categories based on specific conditions.
New bounds found for eigenvalues of Laplace operator in Lorentz-Minkowski space.
problem Eigenvalue bounds for spacelike submanifolds in Lorentz-Minkowski space do not match Euclidean space results.
method Developed a new integral formula on compact spacelike sections of the light cone in L m \mathbb{L}^m L m to prove extrinsic upper bounds. result Eigenvalue achieves upper bounds if and only if submanifold lies minimally in certain hypersphere.
Derives path integrals for perturbative strings on various backgrounds.
problem Calculating path integrals for strings on curved backgrounds.
method Derives path integrals from string geometry theory by considering fluctuations around string backgrounds.
result Derives path integrals of all order perturbative strings on various backgrounds.
A general theory of rigid completely integrable analytic partial differential equations is endeavoured. The tube over the light cone in C^3 is shown to be the unique model (up to biholomorphisms) having CR automorphism group of maximal dimension equal to 10. Explicit formulas for the Lie prolongation of vector fields t…
Topological string theory derived from string geometry for non-perturbative effects.
problem Deriving non-perturbative effects in string theory.
method Formulating topological string geometry theory and deriving the partition function from fluctuations around a classical solution.
result Perturbative partition function of topological string theory derived.
Identifies all perturbative vacua in bosonic string theory.
problem Identifying all perturbative vacua in bosonic string theory.
method Completely identified perturbative vacua through string fluctuations.
result Derivation of path-integrals up to any order from fluctuations.
We show that finiteness of the Lorentzian distance is equivalent to the existence of generalised time functions with gradient uniformly bounded away from light cones. To derive this result we introduce new techniques to construct and manipulate achronal sets. As a consequence of these techniques we obtain a functional …
String geometry theory connects strings to space-time and finds string vacua.
problem Identify and find the global minimum of the string vacuum.
method Identify perturbative vacua, derive path-integrals, and solve the global minimum using analytical and numerical methods.
result The global minimum of the effective potential is the string vacuum.
Derives path-integrals for superstrings on curved backgrounds using string geometry theory.
problem Calculating path-integrals for superstrings on curved backgrounds.
method Derives path-integrals from string geometry theory by considering fluctuations around string backgrounds.
result Derives path-integrals for perturbative superstrings on all string backgrounds.
This paper classifies virtual string links up to cobordism using group theory.
problem Classifying virtual string links up to cobordism.
method Using group theory, specifically the group Z n ( n − 1 ) \mathbb{Z}^{n(n-1)} Z n ( n − 1 ) . result Virtual string links up to cobordism are classified by elements of Z n ( n − 1 ) \mathbb{Z}^{n(n-1)} Z n ( n − 1 ) . Revisits elastic string model to explain interest rate correlations.
problem Describing the forward interest rate curve using an elastic string model.
method Reinterprets Baaquie and Bouchaud's (2004) model to highlight market forces.
result Model accurately reproduces FRC correlation structure with minimal parameters.
Chiral string integrands simplify to ambitwistor string integrands in the tensionless limit.
problem Understanding the relationship between chiral and ambitwistor string integrands.
method Analyzing the tensionless limit of chiral superstring integrands.
result Chiral superstring integrands reduce to ambitwistor string integrands in the tensionless limit.
A virtual string can be defined as an equivalence class of planar diagrams under certain kinds of diagrammatic moves. Virtual strings are related to virtual knots in that a simple operation on a virtual knot diagram produces a diagram for a virtual string. In this paper we consider three operations on a virtual string …
A virtual string is a scheme of self-intersections of a closed curve on a surface. We study algebraic invariants of strings as well as two equivalence relations on the set of strings: homotopy and cobordism. We show that the homotopy invariants of strings form an infinite dimensional Lie group. We also discuss connecti…
Research extends Cahn's results on virtual strings to connected non-parallel strings.
problem Understanding the homotopy of virtual strings and their minimal representatives.
method Generalization of Cahn's results using stabilizations, destabilizations, and homotopies.
result Kadokami's statement about virtual strings holds for connected non-parallel strings but not for all strings.
New formulas link string bordism to integers.
problem Understanding the third string bordism group.
method Geometric string structures and 3d TQFT.
result Integral formulas realize the string bordism isomorphism.
There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field theory combined.