Spin TFTs created by gauging line defects in 3D.
problem Creating spin TFTs from oriented TFTs with framed line defects.
method Constructing a spin TFT from an oriented TFT with framed line defects and a commutative Frobenius algebra.
result Spin TFTs extend earlier classifications and reproduce abelian spin Chern-Simons theories.
This paper generalizes two facts about oriented 3d TFTs to the unoriented case. On one hand, it is known that oriented 3d TFTs having a topological boundary condition admit a state-sum construction known as the Turaev-Viro construction. This is related to the string-net construction of fermionic phases of matter. We sh…
Graph coloring is explained using a topological field theory with defects.
problem Graph coloring as a combinatorial problem is quantum in nature.
method Topological field theory with defects to interpret graph coloring.
result Graph coloring is related to sections of a certain bundle.
Adaptive TFTs improve cryptocurrency price prediction accuracy.
problem Precise short-term price prediction in volatile cryptocurrency markets.
method Dynamic subseries lengths and pattern-based categorization.
result Significantly outperforms baseline models in prediction accuracy and profitability.
Multi-horizon forecasting problems often contain a complex mix of inputs -- including static (i.e. time-invariant) covariates, known future inputs, and other exogenous time series that are only observed historically -- without any prior information on how they interact with the target. While several deep learning model…
A modular functor is constructed from non-semisimple 3d TFTs.
problem Constructing modular functors from non-semisimple 3d topological field theories.
method Using a 3d TFT defined in [arXiv:1912.02063], a symmetric monoidal 2-functor is constructed from a 2-category of bordisms to a 2-category of finite linear categories.
result A modular functor is explicitly described as a symmetric monoidal 2-functor.
Automates fitting semiconductor device models using approximate Bayesian computation.
problem Manual tuning of parameters for fitting TFT models to experimental data is inefficient and prone to errors.
method Approximate Bayesian Computation (aBc) for generating posterior distributions of estimated parameters.
result The proposed method accurately predicts model parameters from mobility curves using gradient boosted trees.
We introduce and study the Wilson loops in a general 3D topological field theories (TFTs), and show that the expectation value of Wilson loops also gives knot invariants as in Chern-Simons theory. We study the TFTs within the Batalin-Vilkovisky (BV) and Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) framework, and the…
This is an introductory review of topological field theories (TFTs) called AKSZ sigma models. The AKSZ construction is a mathematical formulation for the construction and analyses of a large class of TFTs, inspired by the Batalin-Vilkovisky formalism of gauge theories. We begin by considering a simple two-dimensional t…
CityTFT models urban building energy using a data-driven approach.
problem Current UBEM methods are time-consuming and based on physics.
method CityTFT uses a TFT framework with an augmented loss function.
result CityTFT predicts energy demands with high accuracy.
Hybrid model improves geopolitical conflict forecasting.
problem Forecasting geopolitical events from sparse, bursty data.
method Sparse Temporal Fusion Transformer (TFT) + Variational Nearest Neighbor Gaussian Process (VNNGP).
result Consistently outperforms standalone TFT in long-range horizons.
Open 2D TFTs extend to closed theories with circle value as Hochschild homology.
problem Extending open 2D TFTs to closed theories.
method Using symmetric monoidal ∞-categories and Hochschild homology.
result Open 2D TFTs admit initial open-closed extensions.
STS clarifies chaos and stochastic dynamics, linking algebraic topology and physics.
problem Chaos and stochastic dynamics in arbitrary form SDEs.
method Supersymmetric theory of stochastic dynamics (STS) using generalized transfer operator (GTO) and topological field theories (TFT).
result Positive 'pressure' in GTOs corresponds to spontaneous breakdown of topological supersymmetry, explaining 1/f noise.
We propose a method to assign non-unitary TQFTs to certain SCFTs, deriving bounds and examples.
problem Assigning non-unitary TQFTs to specific SCFTs of rank 0.
method Using degenerate limits of SCFTs, extracting modular data from supersymmetric partition functions, and proposing a dictionary.
result Deriving a lower bound on the free energy of SCFTs and showing it is saturated by a specific SCFT.
We construct a gauge fixed action for topological membranes on G2-manifold such that its bosonic part is the standard membrane theory in a particular gauge. We prove that quantum mechanically the path-integral in this gauge localizes on associative submanifolds. Moreover on M×S1 the theory naturally reduces…
The compact exceptional Lie groups F4, E6, E7 and E8 have spinor groups as a subgroup as follows: E8 \supset Ss(16) \supset Spin(15) \supset Spin(14) \supset Spin(13), E7 \supset Spin(12) \supset Spin(11), E6 \supset Spin(10), F4 \supset Spin(9) \supset Spin(8) \supset Spin(7) \supset \cdot \cdot \cdot \supset Spin(1) …
The paper explores spin^h structures and their obstructions.
problem Understanding which manifolds are spin^h.
method Analyzing the fifth Stiefel-Whitney class and constructing generalised spin structures.
result Every compact orientable manifold of dimension 7 or lower is spin^h, and there are higher-dimensional manifolds that are not.
Study mSpin(7)-dDT connections on manifolds with mSpin(7)-structures.
problem Understanding moduli spaces of mSpin(7)-dDT connections. method Introduced and studied mSpin(7)-dDT connections using fully nonlinear PDEs. result Moduli space MmSpin(7)′ has finite expected dimension and smoothness under certain conditions. New Spin(7)-instantons constructed on Joyce's manifold.
problem Constructing Spin(7)-instantons on Joyce's compact manifold. method Gluing non-flat connections on local model spaces to a flat connection on the Spin(7)-orbifold. result More than 20,000 new four-parameter families of Spin(7)-instantons. This is an introduction to the construction of higher-dimensional knots by spinning methods. Simple spinning of classical knots was introduced by E. Artin in 1926, and several generalizations have followed. These include twist spinning, superspinning or p-spinning, frame spinning, roll spinning, and deform spinning. We…
New mSpinh-manifolds studied for their properties.
problem Understanding new manifold classifications.
method Exploring mSpinh-manifolds as a new category. result Highlights of mSpinh-manifolds discussed. Study on harmonic flow of Spin(7)-structures in 8D manifolds.
problem Comparing isometric Spin(7)-structures.
method Developed a notion of harmonicity for Spin(7)-structures and studied the harmonic flow.
result Analytical properties of the harmonic flow of Spin(7)-structures presented.
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.
The paper characterizes new invariant spinr spinors on projective spaces.
problem Characterizing new invariant spinr spinors on projective spaces. method Adapting spin representation via exterior forms to the generalised spinr context. result Complete description of the space of invariant spinr spinors for CPn, HPn, and OP2. Spin(7) geometry linked to multisymplectic geometry.
problem Understanding Spin(7) structures through multisymplectic geometry.
method Utilized Spin(7) identities to prove non-degeneracy of Cayley four-form in multisymplectic context.
result Spin(7) geometry is a special case of multisymplectic geometry.
We define spin frames, with the aim of extending spin structures from the category of (pseudo-)Riemannian manifolds to the category of spin manifolds with a fixed signature on them, though with no selected metric structure. Because of this softer requirements, transformations allowed by spin frames are more general tha…
We explore differential and algebraic operations on the exterior product of spinor representations and their twists that give rise to cohomology, the spin cohomology. A linear differential operator d is introduced which is associated to a connection ∇ and a parallel spinor ζ, ∇ζ=0, and the algebraic o…
Proves almost flat spin^c manifolds bound compact manifolds.
problem Proving almost flat spin^c manifolds bound compact manifolds.
method Long-standing conjecture of Farrell--Zdravkovska and S. T. Yau settled.
result Every almost flat spin^c manifold bounds a compact orientable manifold.
Rigidity of elliptic genera proven for non-spin manifolds with S1-action.
problem Rigidity of elliptic genera for non-spin manifolds with S1-action. method Analysis of universal covering spin condition and π2(M) for rigidity. result Rigidity of elliptic genera is proven for spin universal coverings but not for non-spin universal coverings.
First non-trivial examples of deformed Spin(7)-instantons constructed.
problem Constructing deformed Spin(7)-instantons and connections.
method Constructing on cotangent bundles of CP2 and cones over 3-Sasakian 7-manifolds. result First non-trivial examples of deformed Spin(7)-instantons.
Study shows certain spin manifolds can't meet DEC condition.
problem Non-existence of spin fill-ins meeting DEC condition.
method Analyzes spin Riemannian manifolds and generalized mean curvature functions.
result Closed spin manifolds cannot satisfy DEC if curvature is large.
The paper explores connections between quaternionic and Cayley calibrations in dimensions 8 and 16.
problem Exploring connections between quaternionic and Cayley calibrations in dimensions 8 and 16.
method Starting from collections of 'Kähler 2-forms', the paper constructs canonical 4-forms and calibrated 4-planes in dimensions 8 and 16.
result Explicit formulas for canonical 4-forms ΦSpin(8) and ΦSpin(7)U(1) are derived, and their calibrated 4-planes are characterized. Joyce constructed examples of compact eight-manifolds with holonomy Spin(7), starting with a Calabi-Yau four-orbifold with isolated singular points of a special kind. That construction can be seen as the gluing of ALE Spin(7)-manifolds to each singular point of the Calabi-Yau four-orbifold divided by an anti-holomorphi…
Real vector bundles are determined by their Dirac indices on specific spin manifolds.
problem Determining real vector bundles using Dirac indices.
method Mapping spin or spinh manifolds into a compact smooth manifold and using Dirac indices. result Real vector bundles are uniquely determined by their Dirac indices on prescribed manifolds.
The paper studies curvature identities and solitons on Spin(7)-manifolds.
problem Curvature identities and solitons on Spin(7)-manifolds.
method Analyzes the curvature and torsion of Spin(7)-manifolds, proving identities and conditions.
result Conditions for closed torsion and implications for Ricci flatness and solitons.
This paper gives a combinatorial description of spin and spin^c-structures on triangulated PL-manifolds of arbitrary dimension. These formulations of spin and spin^c-structures are established primarily for the purpose of aiding in computations. The novelty of the approach is we rely heavily on the naturality of binary…
Paper proposes a method for weather-informed probabilistic forecasting and scenario generation in power systems.
problem Challenges of integrating renewable energy sources into power grids due to their stochasticity and uncertainty.
method Combines probabilistic forecasting and Gaussian copula for day-ahead prediction and scenario generation of load, wind, and solar power.
result Demonstrates superior performance of the proposed weather-informed Temporal Fusion Transformer (WI-TFT) model.
No spin structures found in a hyperbolic 4D space.
problem Finding hyperbolic 4-manifolds without spin structures.
method Constructed a non-compact, orientable, hyperbolic 4-manifold.
result Demonstrated existence of a hyperbolic 4D space without spin structures.
New invariant for spin 3-manifolds using super 3-cocycles.
problem Constructing an invariant for spin 3-manifolds.
method State sum construction based on super 3-cocycles and combinatorial representation.
result The invariant is sensitive to the spin structure.
Let J be the exceptional Jordan algebra over R and J^C its complexification. Then the simply connected compact exceptional Lie group F_4 acts on J and F_4 has three orbit types which are F_4/F_4, F_4/Spin(9), F_4/Spin(8). Similarly the simply connected compact exceptional Lie group E_6 acts on J^C and E_6 has five orbi…
Study invariant spin^r structures on homogeneous spaces.
problem Classify invariant spin^r structures on homogeneous spaces.
method Introduce and study G-invariance of spin^r structures on homogeneous spaces. result Classification of invariant spin^r structures in terms of isotropy representation.
Classifies Spin(7) structures on compact 8-manifolds with abelian fundamental group.
problem Classifying Spin(7) structures on compact 8-manifolds.
method Obstruction theory applied to Spin(7) structures on compact 8-manifolds with abelian fundamental group.
result Compact Riemannian 8-manifolds with holonomy Spin(7) have exactly two Spin(7) structures extending the induced G2 structure on the boundary.
Based on a pair of cohomology operations on so called δ−2-formal spaces, we construct the integral cohomology rings of the classifying spaces of the Lie groups Spin(n) and Spinc(n). As applications, we introduce characteristic classes for the reduced topological KSpin theory, determine the ring of integra…
Classifies invariant spin structures on spheres.
problem Determining which Lie groups preserve the unique spin structure.
method Two approaches: differential of actions and representation theory.
result Classification of Lie groups preserving the spin structure.
Simplified proof of spin^c structures using twistor spaces.
problem Proving every compact oriented 4-manifold admits spin^c structures.
method Using twistor spaces to provide a simpler, more geometric proof.
result Simplified and clarified understanding of spin^c structures in 4-manifolds.
Researchers compute mod 2 Seiberg-Witten invariants for spin structures and families.
problem Computing mod 2 Seiberg-Witten invariants for spin structures and families.
method Using Pin(2)-symmetry and localisation in equivariant cohomology, the researchers enhance and compute the invariants.
result The mod 2 Seiberg-Witten invariants are computed for spin structures and families, confirming the simple type conjecture mod 2.
Spin Lefschetz fibrations can represent any group and lattice point.
problem Representing groups and lattice points using Lefschetz fibrations.
method Proving any finitely presented group and admissible lattice point can be realized as a spin Lefschetz fibration.
result Spin Lefschetz fibrations can represent any group and lattice point.
In this paper, we extend the study of generalized Killing spinors on Riemannian Spinc manifolds started by Moroianu and Herzlich to complex Killing functions. We prove that such spinor fields are always real Spinc Killing spinors or imaginary generalized Spinc Killing spinors, providing that the dimension of t…