Study extends Higgs bundle theory to Sasakian manifolds.
problem No direct problem stated, but extends theory to new manifold types.
method Extends Donaldson-Corlette-Hitchin-Simpson correspondence to Sasakian manifolds.
result Establishes correspondence between Higgs bundles and flat connections on Sasakian manifolds.
The Kapustin-Witten equations relate to nonabelian Hodge theory on Kähler surfaces.
problem Relating Kapustin-Witten equations to nonabelian Hodge theory.
method Utilizing nonabelian Hodge theory correspondence to describe moduli spaces.
result Computing expected dimension of moduli spaces for Kapustin-Witten equations.
Base of fibered correspondence is arbitrary correspondence. Fibered correspondence is interesting when we consider relationship between different bundles. However composition of fibered correspondences may not always be defined. Reduced fibered correspondence is defined only between fibers over the same point of base. …
Generalizes uniformization to algebraic correspondences.
problem Uniformizing non-homeomorphic genus zero orbifolds.
method Constructs algebraic correspondences to simultaneously uniformize orbifolds.
result Realizes Teichmüller space of a punctured sphere in correspondences.
Study of holomorphic correspondences combining entire maps and Fuchsian groups.
problem Understanding dynamics of entire maps and their interactions with Fuchsian groups.
method Systematic study of (∞:∞) holomorphic correspondences arising from conformal combinations of transcendental entire maps and Fuchsian groups. result The resulting correspondence is the composition of a Möbius involution and the deleted covering correspondence of a meromorphic function with a simple pole.
Introduces non-abelian Hodge correspondence linking algebraic structures to geometry.
problem None explicitly stated, focuses on introduction.
method Pedagogical introduction of concepts linking algebraic structures to geometry.
result Explains the non-abelian Hodge correspondence and its connections.
New geometric proof for rational tangles links-quivers correspondence.
problem Recovering symmetric/antisymmetric colored HOMFLY-PT polynomials from a quiver.
method Geometric approach using winding numbers in punctured plane and its second configuration space.
result Explicit description of quivers for rational tangles.
Generalizes HK/QK correspondence to para-geometries.
problem Tackles the HK/QK correspondence in para-geometries.
method Provides a new proof and constructs deformations.
result Shows quaternionic Kahler target manifold for para-geometries.
The paper defines a category of Lagrangian correspondences in super Hilbert spaces and constructs a functorial field theory.
problem Understanding composition of Lagrangian correspondences in Hilbert spaces.
method Study of Lagrangian correspondences, construction of a category, and functorial field theory.
result Well-defined composition law in a category of Lagrangian correspondences.
Classical-quantum correspondence on hyperbolic manifolds established.
problem Classical-quantum spectrum correspondence on hyperbolic manifolds.
method Direct correspondence between geodesic flow and Laplacian spectra.
result Established correspondence for convex cocompact hyperbolic manifolds.
Proves isometric correspondence of leaves for generic rolling distributions.
problem Isometric correspondence of leaves in generic rolling distributions.
method Uses Bäcklund transformation for proof.
result Requires Bäcklund transformation for isometric correspondence of leaves.
Constructs correspondences on hyperelliptic surfaces combining orbifold groups and Blaschke products.
problem Combining geometric and dynamical properties on hyperelliptic surfaces.
method Analytic combinations on Riemann sphere, algebraic characterization, and Teichmüller spaces.
result Explicit description of correspondences and injection into Hurwitz spaces.
With respect to the Dolbeault complex over the flat manifold $\C^n$, an explicit description of the inverse correspondence of the twistor correspondence is given.
Geometrically describes Higgs bundle moduli spaces for orthogonal groups.
problem Understanding moduli spaces of Higgs bundles for orthogonal groups.
method Cayley and Langlands type correspondences for real orthogonal and symplectic Higgs bundles.
result Complete abelianization of real slices for all quasi-split real forms.
The calculus correspondence has been known to exist between generic pedal evolutions and generic wave front evolutions. In this paper, we first extend the known results on the calculus correspondence to evolutions with multi-parameters, and then give applications of calculus correspondence. Moreover, we discuss the pos…
Study Kobayashi-Hitchin correspondence for special sheaves on Kähler manifolds.
problem Understanding the Kobayashi-Hitchin correspondence for specific sheaves.
method Using Hermitian-Yang-Mills flow on Kähler manifolds with simple normal crossing divisors.
result Established the correspondence for saturated reflexive parabolic sheaves.
Constructs Lagrangian correspondences for Higgs bundles and holomorphic connections.
problem Realizing geometric Langlands correspondences for Higgs bundles and connections.
method Using transversal Higgs bundles and holomorphic connections, induced divisors and parameters.
result Evidence suggests generic realization of Dolbeault geometric Langlands correspondence.
The paper extends Riemann-Hilbert correspondence to foliations.
problem Understanding representations of Lie algebroids and groupoids in foliated settings.
method Establishing an A∞ de Rham theorem and constructing an integration functor. result An equivalence between ∞-representations of L∞-algebroids and ∞-representations of Lie ∞-groupoids for foliations. ROBOT framework solves regression without correspondence for large data and complex models.
problem Regression without known correspondence in large datasets.
method ROBOT framework reformulates regression as a continuous optimization problem and uses hypergradient approach.
result ROBOT achieves better performance than existing methods in linear and nonlinear regression tasks.
Paper establishes a discrete correspondence between CMC surfaces in R^3 and minimal surfaces in S^3.
problem No specific problem stated; focuses on mathematical correspondence.
method Discrete isothermic surfaces and Lax matrices.
result Preservation of metric coefficients and immersion formulas in discrete case.
In this paper, we define the corresponding submanifolds to left-invariant Riemannian metrics on Lie groups, and study the following question: does a distinguished left-invariant Riemannian metric on a Lie group correspond to a distinguished submanifold? As a result, we prove that the solvsolitons on three-dimensional s…
Overview of dynamics in algebraic correspondences and their connections.
problem Understanding dynamics in algebraic correspondences and their connections.
method Focus on matings between rational maps and Kleinian groups, highlighting unifying structures.
result Rich dynamics and connections between moduli spaces of rational maps and Kleinian groups.
Taxicab correspondence analysis visualizes sparse text data sets.
problem Visualization of extremely sparse contingency tables.
method Robust variant of correspondence analysis for sparse data.
result Visualized an 8265-dimensional textual data set.
Proves Giroux Correspondence in 3D using Heegaard splittings.
problem Proving Giroux Correspondence in 3D contact manifolds.
method Uses Heegaard splittings of contact manifolds, extending convex surface theory.
result Accessible proof for low-dimensional audience.
Extends Calabi's correspondence to φ-minimal graphs in R3.
problem Extending Calabi's correspondence to φ-minimal graphs. method Using a two-parametric group of translations for φ-invariant functions. result New applications in studying φ-minimal graphs. In this paper, we want to construct a one-to-one correspondence from the set of diffeomorphism classes of spin d-twisted homology $\mc P^3$ to the set of isotopy classes of the embedding from S3 to S6, which is a generalization of the Montgomery-Yang correspondence. Furthermore, we will apply this generalized c…
Proves correspondence between harmonic and Higgs bundles.
problem Connecting harmonic and Higgs bundles for study.
method Kobayashi-Hitchin correspondence for polystable bundles.
result Establishes correspondence between good wild harmonic bundles and polystable good filtered λ-flat bundles. We show Mckay correspondence of Betti numbers of Chen-Ruan coho- mology for omnioriented quasitoric orbifolds. In previous articles with M. Poddar [8], [9], we proved the correspondence for four dimension and six dimensions. Here we deal with the general case.
Survey on Higgs bundles via harmonic maps and their role in non-abelian Hodge correspondence.
problem Understanding the non-abelian Hodge correspondence and equivariant harmonic maps.
method Explains the non-abelian Hodge correspondence and reviews progress on equivariant harmonic maps.
result Review of current progress on open problems in equivariant harmonic maps.
Paper extends Kobayashi-Hitchin correspondence to non-Kähler manifolds.
problem Applying Kobayashi-Hitchin correspondence to non-Kähler manifolds.
method Continuity method for vortex equation, Kobayashi-Hitchin correspondence for holomorphic pairs.
result Proved solvability of vortex equation on holomorphic vector bundles over compact Hermitian manifolds.
New correspondence links fluxless to fluxy flag manifolds via T-duality.
problem Understanding fluxes on flag manifolds.
method Defining a new correspondence and using infinitesimal T-duality.
result Infinitesimal T-duality generates nontrivial fluxes.
Paper defines almost flat relative bundles and their correspondence with quasi-representations.
problem Understanding the equivalence of topological and smooth almost flatness.
method Introduces almost flatness for relative bundles, proves equivalence, and defines correspondence with quasi-representations.
result Equivalence of topological and smooth almost flatness and construction of almost flat bundles.
New construction generalizes quaternionic Kähler/hyper-Kähler correspondence.
problem Constructing hypercomplex manifolds from quaternionic ones.
method Constructing hypercomplex manifold M′ from quaternionic manifold M with U(1)-symmetry. result Obtained a compact homogeneous hypercomplex manifold without hyper-Kähler structure.
A neural architecture learns and refines graph correspondences.
problem Learning structural correspondences between graphs.
method Two-stage neural architecture: node embeddings followed by message passing networks.
result Message passing scheme computes well-founded consensus for corresponding neighborhoods.
We generalize Lagrangian Floer cohomology to sequences of Lagrangian correspondences. For sequences related by the geometric composition of Lagrangian correspondences we establish an isomorphism of the Floer cohomologies. We give applications to calculations of Floer cohomology, displaceability of Lagrangian correspond…
For a given lattice, we establish an equivalence involving a closed zone of the corresponding Voronoi polytope, a lamina hyperplane of the corresponding Delaunay partition and a quadratic form of rank 1 being an extreme ray of the corresponding L-type domain.
The Kobayashi-Hitchin correspondence is proven for twisted vector bundles on Kähler manifolds.
problem Proving the Kobayashi-Hitchin correspondence for twisted holomorphic vector bundles.
method Proved the correspondence and approximate correspondence for twisted holomorphic vector bundles on compact Kähler manifolds.
result A twisted holomorphic vector bundle is g−polystable if and only if it is g−Hermite-Einstein, and g−semistable if and only if it is approximate g−Hermite-Einstein. Paper proposes neural networks for fundamental matrix estimation without key-point correspondences.
problem Estimating fundamental matrices from noisy and unreliable key-point correspondences.
method End-to-end neural network architectures preserving fundamental matrix properties.
result Neural networks achieve competitive performance on the KITTI dataset without correspondences.
Isomorphism found between Floer homology and contact geometry.
problem Connecting Floer homology and contact geometry.
method Demonstrated isomorphism between strand algebra and contact category.
result Direct correspondence between Floer homology and contact geometry concepts.
Study of monopoles and q-difference modules correspondence.
problem Finding a correspondence between algebraic and differential geometric objects.
method Analogue of non-abelian Hodge theory for q-difference modules. result Doubly periodic monopoles and parabolic q-difference modules correspond. We construct examples of singular self-dual Zollfrei metrics explicitly, by patching a pair of Petean's self-dual split-signature metrics. We prove that there is a natural one-to-one correspondence between these singular metrics and a certain set of embeddings of RP3 to CP3 which has one singular point. This embe…
An integral hyperbolic lattice is called reflective if its automorphism group is generated by reflections, up to finite index. Since 1981, it is known that their number is essentially finite. We show that K3 surfaces over C with reflective Picard lattices can be characterized in terms of compositions of their self-corr…
Graph matching recovers lost vertex correspondence in shuffled graphs.
problem Errorful vertex correspondences impact graph inference performance.
method Information theory and graph matching algorithms.
result Graph matching can recover true vertex correspondence and reduce information loss.
The paper explains geometric correspondences for homothetic navigation.
problem Understanding geodesic and Jacobi field correspondences in homothetic navigation.
method Providing conceptual explanations and shortcuts to formulas.
result Directly seeing local correspondence between isoparametric functions or hypersurfaces.
Correspondence found between exponential families and affine Grassmannians.
problem Understanding the relationship between exponential families and geometric structures.
method Established a one-to-one correspondence between exponential families and affine Grassmannians.
result Found a correspondence between minimal exponential families and affine Grassmannians.
Holonomies match for higher local systems and principal 2-bundles.
problem Matching holonomies for higher local systems and principal 2-bundles.
method Higher Riemann-Hilbert correspondence and principal 2-bundles.
result Holonomies coincide for both formalisms.
The paper establishes a correspondence between Higgs torsors and connections on curves.
problem Establishing a correspondence between Higgs torsors and connections on curves.
method Introduced a stability condition on filtered Stokes local systems and used it to prove a one-to-one correspondence.
result One-to-one correspondence between stable meromorphic parahoric Higgs torsors and stable meromorphic parahoric connections.
Study proves correspondence for special bundles on complex surfaces.
problem Proving correspondence for parabolic bundles on complex surfaces.
method Kobayashi-Hitchin correspondence for parabolic bundles over compact non-Kähler surfaces.
result Proved Kobayashi-Hitchin correspondence for specified bundles.