Surveying isoparametric foliations and related geometric constructions.
problem Constructing isoparametric foliations using Clifford algebra.
method Representation theory of Clifford algebra and mean curvature flow.
result Investigation of geometric constructions related to isoparametric hypersurfaces.
Geometric model for Hodge filtered complex cobordism constructed.
problem Constructing a geometric model for Hodge filtered complex cobordism.
method Refinement of Pontryagin-Thom construction to create an explicit isomorphism.
result Explicit isomorphism between geometric and abstract models for complex manifolds.
New geometric measure simplifies complex analysis.
problem Complex geometric analysis challenges.
method Geometric integration and convergence methods.
result Smallest measure satisfying Area Formula.
Constructs knots from 3-manifolds with specified geometric limits.
problem Build knots from 3-manifolds with specific geometric properties.
method Constructs explicit families of knots converging to specified 3-manifolds.
result Constructs knots from geometrically finite 3-manifolds with one end.
Paper explores deformations of Hirota equation using geometric constructions.
problem Dispersionless Hirota equation and its deformations.
method Geometric constructions on twistor space.
result Produces new deformations of Hirota equation.
Develops a new geometric cobordism theory using smooth Thom stacks.
problem Creating a versatile geometric cobordism theory for various geometric data.
method Introducing smooth Thom stacks and identifying a smooth representative of the Thom functor.
result The new theory generalizes parametrized cobordism and includes families of geometric data.
Geometrically constructs dilogarithm from Chern-Simons theory.
problem Dilogarithm function and its properties.
method Spin Chern-Simons invariant of C*-connections.
result Geometric proofs of dilogarithm identities and branching structure.
This is the second paper in a series of papers aimed at providing a geometric construction of modular functors and topological quantum field theories from conformal field theory building on the constructions in [TUY] and [KNTY]. We give a geometric construct of a modular functor for any simple Lie-algebra and any level…
Study on projective structures linked to Hitchin representations.
problem Understanding the topology and geometric properties of projective structures.
method Using gauge theory, flat bundles, Higgs bundles, and geometric constructions.
result Some projective structures are fibered in a standard way.
The study constructs geometrically decomposable aspherical 4-manifolds with non-zero signature and explores their properties.
problem Characterizing geometrically decomposable aspherical 4-manifolds with non-zero signature.
method Constructing examples and proving inequalities for geometrically decomposable aspherical 4-manifolds.
result All geometrically decomposable aspherical 4-manifolds with non-zero signature satisfy the inequality \( \chi \geq 3|σ| \).
New integrators preserve geometric structure in Hamiltonian systems.
problem Preserving geometric structure in Hamiltonian systems on Jacobi manifolds.
method Combining Poissonization and symplectic bi-realizations to construct structure-preserving integrators.
result Explicit construction and application of Jacobi Hamiltonian integrators.
Geometrically solves Schrödinger flow on sphere.
problem Solving periodic Cauchy problem for Schrödinger flow on sphere.
method Explicit geometric algorithm for construction of solutions.
result Explicit geometric algorithm for solving Schrödinger flow on sphere.
Extends Satoh's map to virtual m-links and constructs geometric pictures.
problem Virtual m-links and their geometric representations.
method Generalization of Satoh's map to virtual m-links and construction of geometric pictures.
result New geometric pictures of virtual m-links.
This paper develops a general method for constructing Poisson integrators.
problem Lack of a general theory for Poisson integrators due to geometric challenges.
method Adapting structural results about symplectic realizations to create geometric approximations.
result Developed a general approach for constructing geometric integrators on Poisson manifolds.
Expanding knowledge of Engel structures via geometric constructions and dynamics analysis.
problem Understanding Engel structures and their geometric properties.
method Developing canonical geometric constructions and analyzing dynamics of Cauchy characteristics.
result Illustrates the elliptic, parabolic, and hyperbolic behaviors of Cauchy characteristics.
Constructs constant mean curvature surfaces using geometric flow.
problem Creating surfaces with constant mean curvature in 3D spaces.
method Using a generalized Weierstrass representation and geometric flow on potentials.
result Describes construction of CMC surfaces with symmetries.
The twist construction is a geometric model of T-duality that includes constructions of nilmanifolds from tori. This paper shows how one-dimensional foliations on manifolds may be used in a shear construction, which in algebraic form builds certain solvable Lie groups from Abelian ones. We discuss other examples of geo…
New construction provides non-trivial representations for geometric quantisation.
problem Geometric quantisation of non-integral symplectic structures.
method Construction from Noncommutative Differential Geometry adapted to diffeology.
result The construction provides non-trivial representations.
The paper explores geometric finiteness in mapping class groups and constructs new examples of these subgroups.
problem Understanding geometric finiteness in mapping class groups and constructing new examples.
method Examined several constructions of subgroups and determined conditions for geometric finiteness.
result Provides new examples of parabolically geometrically finite and reducibly geometrically finite subgroups.
New geometric examples of involutions on Hilbert square K3 surfaces.
problem Existence of non-symplectic involutions on Hilbert square K3 surfaces.
method Geometric constructions of involutions on IHS manifolds.
result New examples of involutions proven to exist.
We construct bi-invariant total orderings of residually torsion-free nilpotent groups by using Chen's iterated integrals. This construction can be seen as a generalization of the Magnus ordering of the free groups, and equivalent to the classical construction which uses an iteration of central extensions. Our geometric…
Geometric structures on 5-manifolds from surface group representations of G2'.
problem Constructing geometric structures on 5-manifolds from G2'-surface group representations.
method Using Higgs bundles and partial flag manifolds of G2' to construct geometric structures.
result Developing maps of geometric structures are the domain of discontinuity.
New binomial model fits all moments to geometric Brownian motion.
problem Discontinuity problem in option pricing.
method Constructs a generalized binomial tree model.
result Resolves discontinuity problem in option pricing.
The B-quadrilateral lattice (BQL) provides geometric interpretation of Miwa's discrete BKP equation within the quadrialteral lattice (QL) theory. After discussing the projective-geometric properties of the lattice we give the algebro-geometric construction of the BQL ephasizing the role of Prym varieties and the corres…
This paper considers "geometric" ideal triangulations of cusped hyperbolic 3-manifolds, i.e. decompositions into positive volume ideal hyperbolic tetrahedra. We exhibit infinitely many geometric ideal triangulations of the figure eight knot complement. As far as we know, this is the first construction of infinitely man…
We present a geometric construction of the exceptional Lie algebras F4 and E8 starting from the round 8- and 15-spheres, respectively, inspired by the construction of the Killing superalgebra of a supersymmetric supergravity background. (There is no supergravity in the paper.)
Constructs geometric models for moduli spaces of Higgs bundles over Riemann sphere.
problem Construction of moduli spaces for Higgs bundles with specific properties.
method Elementary geometric and combinatorial techniques, focusing on orbit stability of automorphism groups.
result Explicit geometric models for moduli spaces of parabolic Higgs bundles over Riemann sphere.
The paper constructs triangulations for double twist knots using geometric methods.
problem Constructing explicit triangulations of double twist knots.
method Using triangulating Dehn fillings, layered solid tori, and their double covers.
result Proves both triangulations are geometric, using conjecturally minimal triangulation to present A-polynomial equations.
We construct the geometric Baum-Connes assembly map for twisted Lie groupoids, that means for Lie groupoids together with a given groupoid equivariant PU(H)−principle bundle. The construction is based on the use of geometric deformation groupoids, these objects allow in particular to give a geometric construction of …
We give a geometric construction of the multivariable Conway potential function for colored links. In the case of a single color, it is Kauffman's definition of the Conway polynomial in terms of a Seifert matrix.
Extends geometric decompositions to arbitrary meshes and forms.
problem Constructing local bases for finite element spaces on arbitrary meshes.
method Generalizes extension operators to arbitrary meshes and forms, showing they yield geometric decompositions.
result Extension operators yield geometric decompositions for arbitrary meshes and forms.
Geometric recursion constructs measurable functions on moduli spaces.
problem Constructing measurable functions on moduli spaces of bordered Riemann surfaces.
method Inductive construction via excisions of pairs of pants, with convergence conditions.
result Geometric recursion produces functions that can be integrated with respect to the Weil-Petersson measure.
Automatically explores geometric loci of curves using software networking.
problem Exploring hyperbolisms and geometric loci of plane curves.
method Parametric equations, Groebner bases, and elimination for deriving polynomial equations.
result Derives new constructions of lemniscates and other geometric loci.
Geometrically constructs representations for quantization on Kähler manifolds.
problem Quantization of Kähler manifolds using Berezin-Toeplitz method.
method Using peak sections to localize Hilbert spaces around points in the large volume limit.
result Geometric construction of representations for Berezin-Toeplitz quantization.
Action of loop groups on Cuntz algebras constructs geometric twists.
problem Defining actions of loop groups on Cuntz algebras.
method Using representations of Cuntz algebras and analytic loop groups to construct actions and bundles.
result Explicit construction of geometric twists in higher K-theory. The paper explores geometric structures on Weil bundles and their canonical lifts.
problem Transfer of geometric structures from a manifold to its Weil bundle.
method Utilizes differential geometric properties and Weil projection to lift structures.
result Demonstrates canonical lifts of various geometric structures to Weil bundles.
Geometrically constructs parallel transport in Wasserstein space.
problem Parallel transport in Wasserstein space.
method Geometric construction of parallel transport along geodesics.
result Geometric parallel transport agrees with earlier formal calculations.
Construct geometric interpretation of Heston model using group quantization.
problem Geometric interpretation of Heston model
method Lifted local Lie groupoid formulation
result Geometric interpretation of Heston pricing operator and Riccati equations
Geometrically constructs BGG resolutions in Lie algebra type A.
problem Constructing BGG resolutions in Lie algebras of type A.
method Geometric construction in singular infinitesimal character.
result BGG resolutions constructed in Lie algebra type A.
We construct Hermitian representations of Lie algebroids and associated unitary representations of Lie groupoids by a geometric quantization procedure. For this purpose we introduce a new notion of Hamiltonian Lie algebroid actions. The first step of our procedure consists of the construction of a prequantization line …
New method for constructing gluing parameterizations in geometric analysis.
problem Constructing gluing parameterizations for anti-self-dual connections.
method Using C1 maps of smooth Banach manifolds with corners. result Provides a method applicable to other nonlinear PDE problems.
Here we generalize the Gromoll-Meyer construction of an exotic 7-sphere by producing geometric models of exotic 8, 10 and Kervaire spheres as quotients of sphere bundles over spheres by free isometric actions. We give a geometric application at the end.
New quadratic forms expand and rotate linear endomorphisms in geometric theory.
problem Understanding the expansion and rotation properties of linear endomorphisms.
method Constructing new quadratic forms based on two-plane rotations.
result Established relations among eigenvalues, eigendirections, and matrix invariants.
Study of 2D Lorentzian anti-de Sitter plane using geometric control theory.
problem Understanding extremal trajectories and reachable set on anti-de Sitter plane.
method Geometric control theory and differential geometry.
result Construction of optimal synthesis and description of Lorentzian distance.
The aim of this paper is two-fold. First, we give a fully geometric description of the HOMFLYPT homology of Khovanov-Rozansky. Our method is to construct this invariant in terms of the cohomology of various sheaves on certain algebraic groups, in the same spirit as the authors' previous work on Soergel bimodules. All t…
The aim of this paper is to create a large geometrical background on the dual 1-jet space J^{1*}(T,M) for a multi-time Hamiltonian approach of the electromagnetic and gravitational physical fields. Our geometric-physical construction is achieved starting only from a given quadratic Hamiltonian function of polymomenta H…
New complex orthogonal structures found on a 3D manifold.
problem Finding new geometric structures on a 3D manifold.
method Constructing uniformizable complex orthogonal and projective structures.
result A manifold has multiple uniformizable complex orthogonal structures.
Geometric wave propagator defined on Riemannian manifolds.
problem Wave equation on Riemannian manifolds.
method Geometric approach to constructing propagator as oscillatory integral.
result Explicit small time asymptotic expansion of subprincipal symbol.