LC-GAP uses localized Coulomb descriptors for accurate molecular potential predictions.
problem Creating accurate molecular potentials for large molecules.
method Combining localized Coulomb matrix representations with Gaussian approximation potential.
result LC-GAP generates accurate potentials for molecules larger than training data with chemical accuracy.
2d GLSM connects Berry connections to Coulomb branch via difference equations.
problem Connecting Berry connections to Coulomb branch via difference equations.
method Boundary 2d GLSM, 3d A-twisted gauge theory, spectral data of monopoles.
result Coulomb branch algebra actions derived from 2d GLSM.
Quantized Coulomb branches linked to skein algebras.
problem Understanding the relationship between quantized Coulomb branches and skein algebras.
method Association of quantized Coulomb branches to surfaces, description of relationship for specific surfaces, formulation of a conjecture.
result A conjecture linking quantized Coulomb branches and skein algebras.
Study quantized Coulomb branches of Jordan quiver gauge theories and their connections to Cherednik algebras.
problem Understanding the structure of quantized Coulomb branches in Jordan quiver gauge theories.
method Proved isomorphisms between quantized Coulomb branches and spherical graded Cherednik and cyclotomic rational Cherednik algebras.
result Quantized Coulomb branches are deformations of subquotients of Yangians of affine gl(1). Defines mathematical Coulomb branches for 3D gauge theories.
problem Mathematical definition of Coulomb branches in 3D gauge theories.
method Provisional mathematical definition based on existing work.
result Provides a new framework for understanding gauge theories.
Defines mathematical Coulomb branches for 3D gauge theories.
problem No specific problem stated; defines mathematical concept.
method Mathematical definition of Coulomb branches for 3D gauge theories.
result Provisional mathematical definition of Coulomb branches.
Study of Hilbert schemes and Coulomb branches of hypertoric varieties.
problem Understanding the geometry and topology of Coulomb branches of hypertoric varieties.
method Investigation of transverse equivariant Hilbert schemes and Hamiltonian reductions, proposing new metrics.
result Coulomb branches of hypertoric varieties can be constructed as Hilbert schemes or Hamiltonian reductions.
Researchers create a partial resolution of Coulomb branches for gauge theories.
problem Understanding partial resolutions of Coulomb branches in gauge theories.
method Constructing partial resolutions as variants of generalized slices in geometric contexts.
result Identified partial resolutions with specific geometric objects.
We calculate the free energy of Coulomb gas systems on Riemann surfaces.
problem Analyzing the free energy of Coulomb gas systems on Riemann surfaces.
method Using bosonization formula and analytic torsion, we derive the asymptotic expansion of the partition function.
result We prove the geometric version of the Zabrodin-Wiegmann conjecture in the determinantal case.
Study quantized SL2-character variety of a once-punctured torus, finding three Coulomb branch isomorphisms.
problem Understanding the structure of quantized SL2-character variety of a once-punctured torus.
method Analyzing the quantized algebra and its subalgebras isomorphic to Coulomb branches.
result Three Z2-invariant subalgebras of the quantized algebra are isomorphic to Coulomb branches. Coulomb GANs optimize GANs to generate diverse samples without mode collapse.
problem GANs often generate only a subset of target distribution modes.
method Model GAN learning as a potential field of charged particles, where generated samples attract training set samples and repel each other.
result Coulomb GANs converge to a single Nash equilibrium that matches the target distribution.
We establish existence and regularity results for normal Coulomb frames in the normal bundle of two-dimensional surfaces of disc-type embedded in Euclidean spaces of higher dimensions.
Floer homology connects to quiver Hecke algebras in Coulomb branches.
problem Understanding the representation theory of quiver Hecke algebras.
method Using Lagrangian Floer homology in multiplicative Coulomb branches.
result Cylindrical KLRW algebras are realized by Floer homology.
Study connects spectral geometry with Coulomb interactions in perforated manifolds.
problem Understanding spectral properties of perforated manifolds and their interactions.
method Optimal convergence rates for Steklov eigenvalues and expansions, derived from Green function and Coulomb-type energy.
result Identified two correction scales for Steklov eigenvalues in dimensions two and three.
Sharp estimate found for global Coulomb gauge connection on compact 4-manifolds.
problem Existence of a global Coulomb gauge connection with finite singularities.
method Introduced a new function space L4,∞ to prove the existence. result Existence of a global section with finite singularities satisfying the Coulomb equation and a sharp estimate.
This paper studies ring objects in equivariant derived Satake category from Coulomb branches.
problem Understanding ring objects in equivariant derived Satake category from Coulomb branches.
method Analyzes morphisms from varieties to affine Grassmannian and studies ring objects in equivariant derived category.
result Various constructions in arXiv:1601.03586 work for arbitrary commutative ring objects.
Study non-asymptotic behavior of Coulomb gas on compact manifolds.
problem Understand the behavior of Coulomb gas on compact manifolds.
method Use Kantorovich-Wasserstein distance, empirical measure, and heat kernel.
result Prove concentration inequality in Kantorovich-Wasserstein distance.
Proposes a Coulomb-like model for international trade flows, fitting real-world data.
problem Describing and predicting international trade flows between countries.
method Formulated a coulomb force model where GDP represents charge and distance is influenced by various factors.
result Developed a trade strength distribution equation that fits real-world data well.
Consider the 3-dimensional N=4 supersymmetric gauge theory associated with a compact Lie group Gc and its quaternionic representation M. Physicists study its Coulomb branch, which is a noncompact hyper-Kähler manifold with an SU(2)-action, possibly with singularities. We give a math…
New method uses Coulomb gases for Monte Carlo integration with reduced errors.
problem Reducing integration errors in numerical algorithms.
method Using Gibbs measures with a large deviations approach.
result Preserves large deviation principle for improved integration.
The paper connects G2-manifolds to Coulomb and Higgs phases of gauge theories.
problem Exploring the physical interpretation of special singularities in G2-holonomy manifolds. method Analyzing desingularizations of orbifold singularities and relating them to gauge theories.
result Shows an isomorphism between moduli spaces of Ricci flat metrics and flat ADE-connections.
This is a companion paper of arXiv:1601.03586. We study Coulomb branches of unframed and framed quiver gauge theories of type ADE. In the unframed case they are isomorphic to the moduli space of based rational maps from CP1 to the flag variety. In the framed case they are slices in the affine Grassmannia…
Tripod spiders' energy control analyzed for Hooke and Coulomb potentials.
problem Control of tripod spiders' energy configurations.
method Morse theory for Hooke potential, stationary charges for Coulomb energy.
result For positive charges in a regular triangle, the domain of robust control is non-void.
New gauge condition fixes L2 metric divergence in hyperbolic monopole spaces.
problem Divergence of L2 metric on hyperbolic monopole moduli spaces. method Alternative gauge-fixing condition inspired by supersymmetry.
result Resulting geometry is hyperbolic hyperkähler, analogous to Euclidean monopole spaces.
Smooth Yang-Mills fields proved in supercritical dimensions.
problem Regularity of weak Yang-Mills connections in high dimensions.
method ε-regularity theorem, Coulomb gauges construction.
result Stationary Yang-Mills fields are smooth away from a small singular set.
In this paper we consider the existence and regularity problem for Coulomb frames in the normal bundle of two-dimensional surfaces with higher codimension in Euclidean spaces. While the case of two codimensions can be approached directly by potential theory, more sophisticated methods have to be applied for codimension…
Study analyzes low-energy behavior of Schrödinger operators with Coulomb potentials.
problem Analyzing the limiting resolvent of Schrödinger operators at low energies.
method Using Vasy's second microlocal approach (Lagrangian approach), uniformly analyzing the resolvent from E=0. result Obtained oscillatory asymptotics for the resolvent output at low energy, differing from short-range cases.
New theorems in 2D and 4D for metrics with curvature or singularity.
problem Proving new versions of Huber theorem in dimensions 2 and 4.
method Using Coulomb frames and Bach tensor conditions to construct conformal metrics.
result Constructs conformal metrics with regularity across singularities in 4D.
Maxwell equations decay to Coulomb solutions on black hole spacetimes.
problem Decay of Maxwell solutions in Schwarzschild-de Sitter spacetimes.
method Differential transformation of Maxwell tensor components, Fackerell-Ipser equation, vector field method.
result Super-polynomial decay rate of Maxwell solutions to Coulomb solutions.
Extends Coulomb gauge existence to non-associative gauge theory.
problem Existence of configurations with divergence-free torsion in non-associative gauge theory.
method Analyzes non-associative gauge theory based on smooth loops and their tangent algebras, proving existence of configurations with divergence-free torsion.
result Proves existence of configurations with divergence-free torsion given a sufficiently small torsion in a Sobolev norm.
Consider the 3-dimensional N=4 supersymmetric gauge theory associated with a compact Lie group G and its quaternionic representation M. Physicists study its Coulomb branch, which is a noncompact hyper-Kähler manifold, such as instanton moduli spaces on R4, SU(2)-monopole moduli spa…
Study on Wasserstein gradient flow for MMD between Coulomb measures.
problem Analyzing the long-time behavior of MMD between probability and target measures using Coulomb kernels.
method Existence of global weak solutions, ultracontractive estimate, regularity analysis, exponential decay proof, defective Polyak-Lojasiewicz inequality.
result Exponential decay of squared MMD toward a uniformly positive target measure on flat torus.
The study shows how to regularize weakly harmonic maps using Sobolev norms and Coulomb frames.
problem Regularity of weakly harmonic maps between Riemannian manifolds.
method New structure equations and Coulomb-frame methods combined with Hardy-BMO duality.
result Sufficient conditions on Sobolev norms ensure full regularity of weakly harmonic maps.
This is a supplement to [arXiv:1503.03676], where an approach towards a mathematically rigorous definition of the Coulomb branch of a 3-dimensional N=4 SUSY gauge theory was proposed. We ask questions on their expected properties, especially in relation to the corresponding Higgs branch, partly motivated b…
The paper recasts Penrose-Sparling's non-Hausdorff twistor space using noncommutative geometry.
problem Reinterpreting Penrose-Sparling's non-Hausdorff twistor space.
method Introduces noncommutative geometry techniques to reinterpret the space, using explicit etale gluing groupoid and convolution algebra.
result The source-adapted cyclic pairing recovers the Coulomb charge, demonstrating the effectiveness of the new algebraic model.
Study improves material similarity measures considering distinctiveness.
problem Improving similarity measures for materials science applications.
method Used machine learning techniques with specific descriptors and kernels.
result Minimizing loss of distinctiveness improves prediction accuracy.
Narasimhan and Ramadas showed that the Gribov ambiguity was maximal for the product SU(2) bundle over S^3. Specifically they showed that the holonomy group of the Coulomb connection is dense in the connected component of the identity of the gauge group. Instead of base manifold S^3, we consider here a base manifold wit…
Monoidal categorifies genus zero skein algebra using K-theory.
problem Relating skein algebra to K-theory.
method Using quantized K-theoretic Coulomb branch and Grothendieck ring of equivariant coherent sheaves.
result Monoidal categorification of the skein algebra.
New method associates topological classes to Sobolev bundles in critical dimensions.
problem No standard topology in critical dimensions for Sobolev bundles.
method Coulomb gauges and strong approximations of smooth connections.
result Topology stabilizes for sequences of Sobolev bundles with bounded Yang-Mills energy.
Study on Yang-Mills fields blow-up in 4D, proving certain configurations impossible.
problem Prohibiting specific configurations of Yang-Mills fields in 4D.
method Expanding connection forms on long cylinders, proving equations relating bubble and limit connections.
result Proves certain configurations of Yang-Mills fields in 4D are impossible.
Study regularity of Schrödinger eigenfunctions with Coulomb-type potentials.
problem Regularity of eigenfunctions for Schrödinger operators with singular potentials.
method Blow-ups of manifolds with corners and Lie manifolds.
result Proves regularity estimates in weighted Sobolev spaces for eigenfunctions.
New G2-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 G2-holonomy from domain walls in 5d theories. We find canonical gauges for higher gauge theories in 2- and 3-gauge theories.
problem Finding good gauges for connections in higher gauge theories.
method Defined Coulomb gauges for 2- and 3-connections in strict 2- and 3-gauge theories.
result Coulomb gauges are essentially unique and linear in critical dimensions.
CoulGAT interprets GAT models by analyzing node interactions.
problem Understanding and interpreting the complex interactions within graph attention networks.
method Developed a CoulGAT framework to analyze and interpret GAT model layers and datasets.
result Extracted node-node and node-feature interactions to define a standard model for graph structure.
Study topological twists of massive SQCD with gauge group SU(2) and 3 or fewer fundamental hypermultiplets.
problem Evaluate topological partition functions of massive SQCD with arbitrary gauge bundles and hypermultiplet masses.
method Develop techniques for evaluating low-energy path integrals on the Coulomb branch.
result Formulate theories for arbitrary gauge bundles on compact four-manifolds.
The paper proves a large deviation principle for Gibbs measures on Polish spaces and applies it to specific cases.
problem Large deviation principles for Gibbs measures on Polish spaces.
method General Laplace principle for non-normalized Gibbs measures, applied to conditional Gibbs measures, Coulomb gases, and Fekete points.
result The Laplace principle is proven and applied to specific cases, providing a deterministic version of Γ-convergence. We study solutions of the Bogomolny equation on R^2\times S^1$ with prescribed singularities. We show that Nahm transform establishes a one-to-one correspondence between such solutions and solutions of the Hitchin equations on a punctured cylinder with the eigenvalues of the Higgs field growing at infinity in a particu…
Survey on recent developments in isometric immersions using PDE techniques.
problem Analyzing isometric immersions with low Sobolev regularity.
method Compensated compactness and Coulomb-Uhlenbeck gauges.
result Weak continuity and stability of Gauss-Codazzi-Ricci equations.