Constructs 2-Hilbert space for line bundle gerbes.
problem Higher prequantisation and line bundle gerbes.
method Constructs a 2-Hilbert space category from morphism categories of line bundle gerbes.
result Shows the constructed 2-Hilbert space is semisimple and abelian.
Abstract: Generalizes prequantization map for 2-plectic manifolds.
problem Generalizing prequantization map for 2-plectic manifolds.
method Constructs a PU(H)-bundle and Lie groupoid over the total space of a manifold with an integral closed 3-form. result Provides a Lie 2-algebra quasi-isomorphism from observables to weak symmetries.
This paper is about the relation of the geometry of Lie groupoids over a fixed compact manifold and the geometry of their (infinite-dimensional) bisection Lie groups. In the first part of the paper we investigate the relation of the bisections to a given Lie groupoid, where the second part is about the construction of …
Develops 2-Hilbert spaces for bundle gerbes in geometric quantization.
problem Higher geometric quantization of bundle gerbes.
method Introduces 2-Hilbert spaces, rig-categories, and duals for bundle gerbes.
result Constructs a 2-Hilbert space of sections for bundle gerbes.
Survey of bundle gerbes in geometry, field theory, and quantization.
problem Exploring bundle gerbes and their applications in geometry, field theory, and quantization.
method Definition and classification of bundle gerbes with connection, surface holonomy, transgression line bundles, and geometric quantization.
result Bundle gerbes provide a smooth bordism-type field theory and geometric quantization for 2-plectic and symplectic forms.
A new gauge principle for string models emerges from groupoid symmetries.
problem Describing gauge symmetries in 2D non-linear sigma models.
method Introducing principaloid bundles and using twisted equivariant structures.
result Emergence of Poisson sigma models from gauge principles.
Paper constructs Chern character for higher twists and shows isomorphism between K-theory and cohomology.
problem Mapping higher twisted K-theory to higher twisted cohomology.
method Constructing Chern character for higher twists and showing isomorphism.
result Chern character gives isomorphism between higher twisted K-theory and higher twisted cohomology.
Higher Gauge Flow Models integrate higher geometry and symmetries into Generative Flow Models.
problem Improving generative models' performance.
method Integrates L∞-algebra into Generative Flow Models, leveraging higher geometry and symmetries. result Substantial performance improvements on Gaussian Mixture Model datasets.
The paper studies higher geometric structures and connections on manifolds, constructing moduli stacks and proving equivalence criteria.
problem Classifying and understanding higher geometric structures and connections on manifolds.
method Constructing smooth higher symmetry groups, moduli stacks, and higher gauge actions; proving equivalence criteria.
result Construction and classification of moduli stacks of higher geometric data and connections.
New method for non-abelian parallel transport in higher gauge theories.
problem Limitation of previous approaches to higher gauge fields, making them locally gauge equivalent to abelian connections.
method Generalizing the notion of higher connection to overcome fake flatness condition.
result Definition of a generalized higher holonomy functor free from fake flatness condition.
Explains model structures for higher orbifolds and applies them to quantum cohomology.
problem Understanding quantum cohomology of higher orbifolds.
method Develops model structures on higher orbifolds and applies them to quantum cohomology.
result Model structures provide insights into quantum cohomology of higher orbifolds.
Study higher order fermionic and bosonic operators on cylinders and Hopf manifolds.
problem Understanding higher order higher spin operators on specific manifolds.
method Analysis of higher order operators on cylinders and Hopf manifolds.
result Construction of kernels for these operators on the studied manifolds.
The thesis uses simplicial methods to study actions, bundles, and bibundles of higher groupoids.
problem Understanding actions, bundles, and bibundles of higher groupoids.
method Employing simplicial methods to model actions, principal bundles, and bibundles of higher groupoids.
result The simplicial definitions agree with categorification approaches and prove a theorem on differentiation of higher Lie groupoids.
Develops higher gauge theory for categorified spaces, solving tensor field equations.
problem Finding non-Abelian self-dual tensor field equations in six dimensions.
method Uses higher groupoids and connections on higher groupoid bundles.
result Obtains six-dimensional superconformal field theories via higher gauge structure.
Defines a higher version of omni-Lie algebroid for new geometries.
problem No specific problem stated; focuses on definition.
method Proposes a new definition of higher omni-Lie algebroid.
result Studies isotropic and involutive subbundles of higher omni-Lie algebroid.
Reductions of higher tangent bundles of Lie groupoids provide natural examples of geometric structures which we would like to call higher algebroids. Such objects can be also constructed abstractly starting from an arbitrary almost Lie algebroid. A higher algebroid is, in principle, a graded bundle equipped with a diff…
Proves rigidity for higher rank three-manifolds without curvature constraints.
problem Rigidity of higher rank three-manifolds without curvature assumptions.
method Analyzes complete Riemannian three-manifolds of higher rank.
result Proves conditions for manifolds to be spherical or hyperbolic space forms.
We classify higher-SPTs and their anomalies via cobordism theory.
problem Understanding higher symmetries and anomalies in quantum field theories.
method Developed a generalized cobordism theory using advanced mathematical tools.
result Classified higher-SPTs and their boundary anomalies.
Generalized Fáry's theorem to higher dimensions.
problem No specific problem stated; generalization of Fáry's theorem.
method Proof of a higher-dimensional version of Fáry's theorem.
result Proved a generalization of Fáry's theorem in higher dimensions.
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.
This note discusses the higher K-energy functionals which were defined by Bando and Mabuchi, and integrate higher Futaki invariants. Two new formulas for the higher K-energy functionals are given, and the second K-energy is shown to be related to Donaldson's Lagrangian applied to metrics on the tangent bundle.
This article reviews ∞-bundles and their applications in geometry and physics.
problem Understanding higher bundles in geometry and physics.
method An ∞-categorical formulation of higher bundles. result Identification of higher bundles in various contexts.
Study of higher-order Dirac structures in field theory.
problem Extending multisymplectic structures to higher-order analogues.
method Define and analyze higher Dirac structures as involutive subbundles of TM+∧kTM∗. result Recover higher Poisson structures as infinitesimal counterparts of multisymplectic groupoids.
Extends higher smooth torsion to twisted cohomology.
problem Defining higher smooth torsion in twisted cohomology.
method Extends Badzioch's, Dorabiala's, and Williams' definition to twisted cohomology.
result Satisfies geometric additivity and transfer in twisted cohomology.
Higher topos theory applied to physics.
problem No specific problem stated.
method Exposition of higher topos theory.
result No specific key result mentioned.
Introduces higher-order clustering coefficients to better understand network structures.
problem Understanding the clustering behavior of higher-order network cliques in complex networks.
method Develops higher-order clustering coefficients as a generalization of traditional clustering coefficients.
result Provides new insights into the structure of real-world networks.
Transformed quadrics from 2D to higher dimensions.
problem Generalizing quadric transformations to higher dimensions.
method Bianchi's Hazzidakis transformation method.
result Generalization to higher dimensional quadrics.
Survey on advanced gauge theory concepts.
problem Understanding higher gauge theory structures.
method Introduction to higher structures and connections on higher principal bundles.
result Summarized applications and principles of higher gauge theories.
Proves limitations of higher-order optimization for convex problems.
problem Limitations of higher-order optimization methods for convex problems.
method Proves polynomial dependence on approximation guarantee and higher-order smoothness parameters.
result Nesterov's accelerated cubic regularization method is nearly tight.
Global Double Field Theory is a higher-dimensional generalization of Kaluza-Klein theory.
problem Formulating a global theory for higher-dimensional gauge fields.
method Generalizing Kaluza-Klein theory to higher principal bundles and higher gauge fields.
result Higher Kaluza-Klein geometry provides a global formulation for Double Field Theory.
We formulate differential cohomology and Chern-Weil theory -- the theory of connections on fiber bundles and of gauge fields -- abstractly in the context of a certain class of higher toposes that we call "cohesive". Cocycles in this differential cohomology classify higher principal bundles equipped with cohesive struct…
Introduces higher algebroids via vector bundle comorphisms.
problem Generalizing Lie algebroids and higher tangent bundles.
method Defines higher algebroids as vector bundle comorphisms of graded-linear bundles with specific axioms.
result Provides natural examples and applications in geometric mechanics.
Affine maps reveal higher rank structures in certain spaces.
problem Characterizing spaces with higher rank structures.
method Using Hadamard spaces with geometric group actions and affine maps.
result Affine maps not dilations indicate higher rank structures.
Graphs improve theorem proving in higher-order logic.
problem Challenges in converting higher-order logic formulas into graph-based representations.
method Used graph neural networks (GNNs) to represent and search higher-order logic.
result GNNs outperform state-of-the-art methods in higher-order theorem proving.
Higher gauge theory via differential nonabelian cohomology
problem Global infrared completion of higher gauge fields
method Maxwell-type higher gauge fields
result Electromagnetic flux quantization
The paper encourages Kleinian group thinking for higher rank Lie groups.
problem No specific problem stated; encouraging new thinking.
method Discussion of Kleinian group ideas applied to higher rank Lie groups.
result Encouragement to think about higher rank Lie groups using Kleinian group theory.
New lattices are linked to higher hypergeometric functions.
problem Understanding non-arithmetic lattices in PU(2,1).
method Showed all known non-arithmetic lattices are monodromy groups of higher hypergeometric functions.
result Non-arithmetic lattices in PU(2,1) are linked to higher hypergeometric functions.
Paper introduces techniques to learn higher-order programs, improving predictive accuracy and reducing learning times.
problem Expressing and learning complex programs in ILP.
method Extending meta-interpretive learning to support higher-order definitions as background knowledge.
result Learning higher-order programs reduces hypothesis space and sample complexity, improving predictive accuracy and reducing learning times.
Proves a higher rank rigidity theorem for convex real projective manifolds.
problem No specific problem stated; focuses on proving a theorem.
method Analogue of Ballmann and Burns-Spatzier's higher rank rigidity theorem.
result Proves a higher rank rigidity theorem for convex real projective manifolds.
Invites readers to explore higher Teichmüller theory.
problem None explicitly stated; focuses on introduction.
method Description and overview of facets.
result Introduces higher Teichmüller theory to readers.
Study of higher spin Killing spinors on 3D manifolds, proving rigidity and providing explicit expressions.
problem Understanding higher spin Killing spinors on 3D manifolds.
method Definition and detailed study of higher spin Killing spinors in arbitrary dimension, focusing on 3D manifolds. Rigidity result and explicit expressions for 3-sphere and 3-hyperbolic space.
result Proved a rigidity result for 3D manifolds admitting higher spin Killing spinors and provided explicit expressions for these spinors.
For certain classes of knots we define geometric invariants called higher-order genera. Each of these invariants is a refinement of the slice genus of a knot. We find lower bounds for the higher-order genera in terms of certain von Neumann ρ-invariants, which we call higher-order signatures. The higher-order genera o…
Defines a transgression functor for higher-dimensional Courant algebroids.
problem None explicitly stated; focuses on definition and properties.
method Definition of transgression functor for Courant algebroids.
result Established a connection between Courant algebroids and Lie algebroids.
The paper explores higher property T in lattices and its connections to geometric phenomena.
problem Understanding higher property T in lattices and related geometric phenomena.
method Operator-algebraic characterizations of higher property T and connections to lattice geometry.
result Unified framework for understanding higher property T and related geometric phenomena.
Introduces new connections in higher geometry.
problem Defining connections in higher geometry.
method Develops formal differentiation and integration of maps to derived stacks.
result Establishes new L∞-algebras of higher symmetries. Proves actions of higher rank lattices on hyperbolic spaces are elementary.
problem Understanding actions of higher rank lattices on hyperbolic spaces.
method Proves actions are either elliptic or parabolic, generalizing tree actions.
result Any morphism from a higher rank lattice to a hierarchically hyperbolic group has finite image.
Paper constructs a transfer map for codimension 2 submanifolds in higher index theory.
problem Higher index theory of codimension 2 submanifolds.
method Construction of codimension 2 transfer map and adjoint relationship with cyclic cohomology.
result Established adjoint relationship between codimension 2 transfer map and co-transfer map in cyclic cohomology.
HONE learns higher-order network embeddings from graph data.
problem Capturing higher-order structures in network data.
method HONE framework based on network motifs, with interchangeable components.
result HONE outperforms other embedding methods by up to 75% in AUC.