Recently we introduced T-duality in the study of topological insulators. In this paper, we study the bulk-boundary correspondence for three phenomena in condensed matter physics, namely, the quantum Hall effect, the Chern insulator, and time reversal invariant topological insulators. In all of these cases, we show that…
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48 results for “bulk-boundary correspondence”
Recently we introduced T-duality in the study of topological insulators, and used it to show that T-duality trivialises the bulk-boundary correspondence in 2 dimensions. In this paper, we partially generalise these results to higher dimensions and briefly discuss the 4D quantum Hall effect.
Einstein metrics on strictly pseudoconvex domains from the viewpoint of bulk-boundary correspondencemath.DG
Survey on Einstein metrics on domains, linking complex geometry to CR structures.
problem Existence of asymptotically complex hyperbolic Einstein metrics.
method Bulk-boundary correspondence between CR structures and Einstein metrics.
result Existence theorems for Einstein metrics on strictly pseudoconvex domains.
We study an asymptotic Dirichlet problem for Weyl structures on asymptotically hyperbolic manifolds. By the bulk-boundary correspondence, or more precisely by the Fefferman-Graham theorem on Poincaré metrics, this leads to a natural extension of the notion of Branson's -curvature to Weyl structures on even-dimension…
Bulk-boundary correspondences and unique continuation in asymptotically Anti-de Sitter spacetimesgr-qc
Research proves unique continuation for Einstein-vacuum equations on aAdS spacetimes.
problem Establishing rigorous mathematical statements for AdS/CFT correspondence.
method Novel Carleman estimates and unique continuation results for wave equations on aAdS spacetimes.
result Proved a unique continuation result for the Einstein-vacuum equations from aAdS conformal boundaries.
Paper connects 3D gravity averages to 2D CFT correlators.
problem Understanding 3D gravity partition functions.
method 3D topological field theories and mapping class group averages.
result Established a correspondence between 3D gravity averages and 2D CFT correlators.
Lower bounds for eigenvalues on manifolds with boundary conditions.
problem Eigenvalue bounds for manifolds with boundary conditions.
method Proving lower bounds for the first non-trivial eigenvalue using Cheeger-type constants.
result Results in the spirit of Cheeger's inequality for manifolds with boundary conditions.
New algorithm constructs characters of rational VOAs from knot complements.
problem Constructing characters of rational VOAs from knot complements.
method 3D gauge theories, Dimofte-Gaiotto-Gukov construction, 3D rank-0 SCFT, topological twist.
result New Nahm-sum-like expressions for Virasoro minimal model characters.
Researchers compute spectral flow of Toeplitz operators on manifolds and domains.
problem Computing spectral flow for families of Toeplitz operators.
method Using Callias-type operators and cohomological formulas, the spectral flow is related to the index of these operators.
result A cohomological formula for spectral flow on even-dimensional manifolds.
On conformally compact manifolds of arbitrary signature, we use conformal geometry to identify a natural (and very general) class of canonical boundary problems. It turns out that these encompass and extend aspects of already known holographic bulk-boundary problems, the conformal scattering description of boundary con…
Geometrically describes parity anomaly in fermionic systems.
problem Parity anomaly in fermionic systems coupled to background fields.
method Functorial quantum field theory, geometric cobordism bicategory, symmetric monoidal bicategories, Atiyah-Patodi-Singer index theorem.
result Explicit computation of 2-cocycle of projective representation.
We propose a family of differential models for B-type open-closed topological Landau-Ginzburg theories defined by a pair , where is any non-compact Calabi-Yau manifold and is any holomorphic complex-valued function defined on whose critical set is compact. The models are constructed at cochain level …
Unified framework for gravity on manifolds with corners.
problem Unified description of gravity on manifolds with corners.
method Derivation of corner Poisson structure, reduction procedure, equivalent affine Poisson description.
result Unified framework for bulk, boundary, and corner structures of Palatini-Cartan gravity.
Unified framework for gravity on manifolds with corners derived.
problem Unified description of gravity on manifolds with corners.
method Derivation of corner Poisson structure and reduction procedure.
result Unified framework for bulk, boundary, and corner structures of Palatini-Cartan gravity.
The paper introduces new CR invariants for pseudo-Einstein manifolds.
problem Constructing CR invariants for pseudo-Einstein manifolds.
method Applying Cheeger-Simons differential characters to a modified normal tractor connection.
result Identifies differential characters with renormalized connections and derives formulas for characteristic numbers.
Fibered Correspondencemath.DG
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.
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…
Kobayashi-Hitchin Correspondence for Saturated Reflexive Parabolic Sheaves on Kähler manifoldsmath.DG
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 de Rham theorem and constructing an integration functor.
result An equivalence between -representations of -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.
Discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3. A discrete Lawson correspondencemath.DG
The main result of this paper is a discrete Lawson correspondence between discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3. This is a correspondence between two discrete isothermic surfaces. We show that this correspondence is an isometry in the following sense: it preserves the metric coefficients int…
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…
Algebraic correspondences and Schwarz reflections: Where rational dynamics meets Kleinian groupsmath.DS
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 -minimal graphs in .
problem Extending Calabi's correspondence to -minimal graphs.
method Using a two-parametric group of translations for -invariant functions.
result New applications in studying -minimal graphs.
We demonstrate an isomorphism between the homology of the strand algebra of bordered Floer homology, and the category algebra of the contact category introduced by Honda. This isomorphism provides a direct correspondence between various notions of Floer homology and arc diagrams, on the one hand, and contact geometry a…
In this paper, we want to construct a one-to-one correspondence from the set of diffeomorphism classes of spin -twisted homology $\mc P^3$ to the set of isotopy classes of the embedding from to , 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 -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 from quaternionic manifold with -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.
Quilted Floer Cohomologymath.SG
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…