We conjecture that the Joyce-Song wall-crossing formula for Donaldson-Thomas invariants arises naturally from an asymptotic expansion in the field theoretic work of Gaiotto, Moore and Neitzke. This would also give a new perspective on how the formulae of Joyce-Song and Kontsevich-Soibelman are related. We check the con…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
Trend · papers per month
48 results for “Wall conjecture”
The present article is the first in a series whose ultimate goal is to prove the Kotschick-Morgan conjecture concerning the wall-crossing formula for the Donaldson invariants of a four-manifold with b^+ = 1. The conjecture asserts that the wall-crossing terms due to changes in the metric depend at most on the homotopy …
Study of stability conditions on 3-folds, focusing on walls and intersections.
problem Understanding stability conditions and numerical walls on 3-folds.
method Differential geometry analysis of numerical walls, proving intersections and maximum turning points.
result Gieseker semistability equivalent to asymptotic semistability along paths in the upper half plane.
The paper proves new results on Poincaré duality pairs and spaces.
problem Establishing Poincaré duality in various contexts and dimensions.
method Analyzes Poincaré spaces and CW pairs, proving relative Poincaré duality and related results.
result Found a finite CW pair where fails to satisfy Poincaré duality in any dimension.
The paper proposes a new way to approximate Riemannian metrics using discrete wall systems.
problem Approximating Riemannian metrics and proving geometric conjectures.
method Discretization of metrics using walls and triangulations.
result The discrete filling area conjecture is equivalent to Gromov's original conjecture.
A smooth compactification of Donaldson moduli spaces is given. As an application, we use this new space to study the wall-crossing formula and prove the Kotschick-Morgan conjecture.
We study the interplay among Wall's problem, normal generation conjecture (the Wiegold Conjecture) of perfect groups and Swan's problem on partial Euler characteristic and deficiency of groups. In particular, for a 3-dimensional complex of cohomological dimension 2 with a finite fundamental group, assuming t…
Quantum dilogarithm function proven from a linear difference equation.
problem Proving Faddeev's quantum dilogarithm from a linear difference equation.
method Proved Faddeev's quantum dilogarithm using Borel summation of a formal power series solution of a linear difference equation.
result Borel summation of a formal power series solution produces Faddeev's quantum dilogarithm.
Given a planar curve singularity, we prove a conjecture of Oblomkov-Shende, relating the geometry of its Hilbert scheme of points to the HOMFLY polynomial of the associated algebraic link. More generally, we prove an extension of this conjecture, due to Diaconescu-Hua-Soibelman, relating stable pair invariants on the c…
The paper computes inertia groups of certain high-dimensional manifolds.
problem Diffeomorphism classification of -connected, smooth, closed, oriented -manifolds.
method Surgery theory, modified surgery, and special cases of conjectures.
result Inertia groups always vanish for and certain cases of .
Predicting the wall-shear stress and wall pressure through convolutional neural networksphysics.flu-dyn
Study uses neural networks to predict wall quantities in turbulent flows.
problem Predicting wall quantities in turbulent open channel flows.
method Training convolutional neural networks (FCN) and a proposed R-Net architecture to predict wall-shear-stress and wall pressure.
result R-Net architecture performs better and predicts wall quantities with around 10% error.
For a smooth projective toric surface we determine the Donaldson invariants and their wallcrossing in terms of the Nekrasov partition function. Using the solution of the Nekrasov conjecture math.AG/0306198, hep-th/0306238, math.AG/0409441 and its refinement math.AG/0311058, we apply this result to give a generating fun…
This paper studies the interplay between the N=2 gauge theories in three and four dimensions that have a geometric description in terms of twisted compactification of the six-dimensional (2,0) SCFT. Our main goal is to construct the three-dimensional domain walls associated to any three-dimensional cobordism. We find t…
New -holonomy manifolds from 5d N=1 theories domain walls.
problem Geometrizing domain walls in 5d N=1 theories.
method Constructing 7-manifolds by fibering a Calabi-Yau over a real line.
result 7-manifolds with -holonomy from domain walls in 5d theories.
We prove an analogue of the Kotschick-Morgan conjecture in the context of SO(3) monopoles, obtaining a formula relating the Donaldson and Seiberg-Witten invariants of smooth four-manifolds using the SO(3)-monopole cobordism. The main technical difficulty in the SO(3)-monopole program relating the Seiberg-Witten and Don…
Study connects Morse theory with cluster variables for wall-crossing in Cerf diagrams.
problem Understanding wall-crossing in Cerf theory.
method Relates Bruhat numbers in real Morse theory to cluster variables in braid varieties.
result Provides wall-crossing coordinates in Cerf diagrams.
We explain how to adapt a construction of M. Sageev's to construct a proper action on a CAT(0) cube complex starting from a proper action on a wall space, and use this to deduce that if G is a group containing an amenable subgroup H of super-polynomial growth and G acts properly on a space with walls then there are arb…
Neural network predicts turbulence near-wall regions efficiently.
problem Reducing computational cost in turbulent flow simulations.
method Fully-convolutional neural network trained on DNS data.
result FCN predicts velocity fluctuations at with less than 20% error.
Farrell and Hsiang noticed that the geometric surgery groups defined By Wall, Chapter 9, do not have the naturality Wall claims for them. They were able to fix the problem by augmenting Wall's definitions to keep track of a line bundle. The definition of geometric Wall groups involves homology with local coefficients a…
The index theorem connects anomalies on a domain wall to global integrals.
problem Relating anomalies on a domain wall to global integrals.
method Formulated and proved an analog of the Atiyah-Patodi-Singer theorem.
result The index is expressed through global chiral and parity anomalies.
Convolutional networks predict turbulence from wall quantities.
problem Predicting turbulence fields from wall-shear-stress components and wall pressure.
method Two CNN models: FCN and FCN-POD, trained on DNS data.
result FCN and FCN-POD models outperform EPOD in predicting turbulence fields.
Conjectures on universal structures in algebraic geometry enumerative invariants.
problem Understanding virtual classes in moduli spaces of stable objects.
method Defining virtual classes in homology over Q and proving a universal wall-crossing formula.
result Proving conjectures for quiver representations using Behrend-Fantechi virtual classes.
The study explores deep and shallow slice knots in 4-manifolds, linking them to conjectures and proving existence and nonexistence results.
problem Understanding slice knots in 4-manifolds and their properties.
method Using Wall self-intersection invariant and Rohlin's result, the study examines various 4-manifolds and their boundaries to find deep slice knots and prove nonexistence results.
result Every 4-manifold with one 0-handle and any number of 2-handles has a deep slice knot in its boundary.
Two 4-manifolds are stably diffeomorphic if they become diffeomorphic after connected sum with S^2 x S^2's. This paper shows that two closed, orientable, homotopy equivalent, smooth 4-manifolds are stably diffeomorphic, provided a certain map from the second homology of the fundamental group with coefficients in Z/2 to…
Analyzes how quadratic differential trajectories change with variation, proving a wall-crossing formula.
problem Analyzing how the number of trajectories of quadratic differentials changes with variation.
method Proves an analytic wall-crossing formula using Fock-Goncharov coordinates and characterizes birational automorphisms.
result Characterizes certain birational automorphisms and computes Stokes automorphisms.
Wall's result extended to 4-manifolds with definite intersection forms.
problem Realizing automorphisms of definite intersection forms.
method Using a specific 4-manifold construction and Wall's original result.
result Automorphisms of definite intersection forms are realized by diffeomorphisms of the constructed 4-manifold.
Extends index theorem to domain walls with discontinuous Riemannian connections.
problem Index theorem for domain walls with discontinuous Yang-Mills and Riemannian connections.
method Extension of index theorem to new conditions.
result Validates index theorem for more complex discontinuities.
Study wall singularities in spaces with upper curvature bounds.
problem Understanding singularities in spaces with curvature constraints.
method Geometric structure theorem and geometric characterization for codimension one and two.
result Necessary and sufficient conditions for singular sets to be of codimension at least two.
Cubulating spaces with wallsmath.GT
We describe a correspondence between spaces with walls and CAT(0) cube complexes.
Prediction of wall-bounded turbulence from wall quantities using convolutional neural networksphysics.flu-dyn
Neural network predicts turbulence from wall shear stress.
problem Predicting wall-bounded turbulence from wall quantities.
method Fully-convolutional neural network trained on DNS data.
result Improved prediction of turbulence fields and statistics.
The purpose of this note is to give a self contained description of Walls finiteness obstruction.
Geometric interpretation of 2d-4d wall-crossing formulas.
problem Understanding wall-crossing phenomena in coupled 2d-4d systems.
method Deformation theory of holomorphic pairs and relation to scattering diagrams.
result Geometric interpretation of wall-crossing formulas.
Modeling aortic wall inhomogeneities to predict dissection risks.
problem Predicting localized stress accumulations in the aortic wall due to inhomogeneities.
method Stochastic constitutive model with random field realizations, coupled with a convolutional neural network surrogate.
result The neural network accurately predicts stress distributions and assesses uncertainty in aortic wall stress.
Proof of wall-crossing formula using spectral networks.
problem Proving the Kontsevich-Soibelman wall-crossing formula.
method Path-lifting rules for spectral networks, convergence justification.
result Definition and justification of path lifting rules for spectral networks.
The paper constructs K-moduli spaces for plane curves and describes wall crossings.
problem Constructing and understanding K-moduli spaces for plane curves.
method Constructing proper good moduli spaces and establishing wall-crossing framework.
result The first wall crossing of K-moduli spaces for plane curves of degree 4 is a weighted blow-up of Kirwan type.
We review our recent work on solitons in the Higgs phase. We use U(N_C) gauge theory with N_F Higgs scalar fields in the fundamental representation, which can be extended to possess eight supercharges. We propose the moduli matrix as a fundamental tool to exhaust all BPS solutions, and to characterize all possible modu…
When formulated in twistor space, the D-instanton corrected hypermultiplet moduli space in N=2 string vacua and the Coulomb branch of rigid N=2 gauge theories on are strikingly similar and, to a large extent, dictated by consistency with wall-crossing. We elucidate this similarity by showing that these…
Abstract: Mapping 3-manifold bordisms to topological orders and domain walls.
problem Mapping spin 3-manifolds to topological orders and their domain walls.
method Defining topological orders from torsion elements in , linking form, and quadratic refinement. Extending to spin bordisms and domain walls.
result Constructing domain walls between topological orders from spin bordisms.
Mathematician-friendly formulation of Atiyah-Patodi-Singer index.
problem Boundary conditions and edge modes in domain-wall fermions.
method Mathematician-friendly derivation of Atiyah-Patodi-Singer index.
result New insights into the interplay of boundary conditions, domain-wall fermions, and edge modes.
Reformulates mod-two APS index using domain-wall fermion.
problem Non-local APS boundary condition and global anomalies.
method Physicist-friendly reformulation of APS index using domain-wall fermion.
result Equivalence between two formulations of APS index.
We study commensurating actions of groups and the associated properties FW and PW, in connection with wallings, median graphs, CAT(0) cubings and multi-ended Schreier graphs.
We use localization formulas in the theory of equivariant cohomology to rederive the wall crossing formulas of Li-Liu and Okonek-Teleman for Seiberg-Witten invariants.
We present a systematic method to construct exactly all Bogomol'nyi-Prasad-Sommerfield (BPS) multi-wall solutions in supersymmetric (SUSY) U(N_C) gauge theories in five dimensions with N_F hypermultiplets in the fundamental representation for infinite gauge coupling. The moduli space of these non-Abelian walls is found…
Deep neural network approximates flow averages for rough walls in multiscale simulations.
problem Approximating flow averages in rough-wall Stokes flow simulations.
method Fourier neural operator for local averages, parameterized by local wall geometry.
result Stable and accurate HMM solution with reduced micro problem solving cost.
Completes classification of high-dimensional manifolds up to exotic sums.
problem Classifying high-dimensional manifolds up to exotic sums.
method Algebraic refinement of intersection forms and Witten genus.
result All but finitely many dimensions are resolved, completing the classification.
We give a physical explanation of the Kontsevich-Soibelman wall-crossing formula for the BPS spectrum in Seiberg-Witten theories. In the process we give an exact description of the BPS instanton corrections to the hyperkahler metric of the moduli space of the theory on R^3 x S^1. The wall-crossing formula reduces to th…
We provide a smoothening criterion for group actions on manifolds by singular diffeomorphisms. We prove that if a countable group has the fixed point property FW for walls (e.g. if it has property (T)), every aperiodic action of by diffeomorphisms that are of class with countably many singularities is con…
The Bogomol'nyi-Prasad-Sommerfield (BPS) multi-wall solutions are constructed in supersymmetric U(N_C) gauge theories in five dimensions with N_F(>N_C) hypermultiplets in the fundamental representation. Exact solutions are obtained with full generic moduli for infinite gauge coupling and with partial moduli for finite …