arXiv research

The paper generalizes Hannay-Berry connections for foliated manifolds with symmetry.

Analyzes Berry phases and connection matrices on Siegel-Jacobi spaces.

Study vortex moduli space and compute Berry curvature for Ginzburg-Landau vortices.

Study Berry connections for 2d GLSMs, linking to cohomology theories.

Study of supersymmetric deformations and monopoles in Kahler geometry.

2d GLSM connects Berry connections to Coulomb branch via difference equations.

A treatment of the spin-statistics relation in nonrelativistic quantum mechanics due to Berry and Robbins [Proc. R. Soc. Lond. A (1997) 453, 1771-1790] is generalised within a group-theoretical framework. The construction of Berry and Robbins is re-formulated in terms of certain locally flat vector bundles over n-parti…

We give sufficient conditions for the existence of a Dirac structure on the total space of a Poisson fiber bundle endowed with a compatible connection. We also show that Cartan and Cartan-Hannay-Berry connections give rise to coupling Dirac structures.

Study local topological constraints on Berry curvature in spin-orbit coupled Bose-Einstein condensates.

A new geometric framework resolves singularities in anomalous transport.

In the space $\mathbb U^4$ of cubic forms of surfaces, regarded as a $G$-space and endowed with a natural invariant metric, the ratio of the volumes of those representing umbilic points with negative to those with positive indexes is evaluated in terms of the asymmetry of the metric, defined here. A connection of this …

Study of 2d gauged linear sigma models to derive difference equations and spectral data.

Kernel smoothing on unknown manifolds with bounds and asymptotic normality.

New statistical test for change-point detection using relative entropy.

Paper improves confidence intervals for LSA with multiplier bootstrap.

Paper develops efficient incomplete U-statistics for degenerate cases.

Deep Gaussian Processes with polynomial kernels can collapse rapidly without proper hyperparameter tuning.

Paper derives convergence rates and confidence intervals for LSA with Markovian noise.

Geometric surgery theory applied to quantum statistics in spacetime.

New bounds for SGD in high dimensions improve inference efficiency.

We explain how the kind of ``parallel transport'' of a wavefunction used in discussing the Berry or Geometrical phase induces the conventional parallel transport of certain real vectors. These real vectors are associated with operators whose commutators yield diagonal operators; or in Lie algebras those operators whose…

Geometric observables detect financial regime shifts with high accuracy.

Study on variance of Laplace eigenfunctions on manifolds.

Paper stabilizes bandit learning with regularization, improving inference under adaptive sampling.

Paper develops robust methods for large-scale testing without tuning parameters.

Mondrian random forests improve statistical inference for regression.

We give a comprehensive theoretical characterization of a nonparametric estimator for the $L_2^2$ divergence between two continuous distributions. We first bound the rate of convergence of our estimator, showing that it is $\sqrt{n}$-consistent provided the densities are sufficiently smooth. In this smooth regime, we t…

Smartphone app counts grapes for accurate yield estimation.

Quantum knots and knotted zeros linked through complex plane mappings.

The paper characterizes the geometry and topology of spin random fields.

Study on volumes of random inscribed polytopes in projective geometries.

QCML uses quantum geometry to represent data.

We give a positive answer to the Berry-Robbins problem for any compact Lie group G, i.e. we show the existence of a smooth W-equivariant map from the space of regular triples in a Cartan subalgebra to the flag manifold G/T. This map is constructed via solutions to Nahm's equations and it is compatible with the SO(3) ac…

The paper provides Gaussian approximations for decentralized Federated Learning.

Researchers extend topological classification to knotted semimetals in 3D.

Tying knots and linking microscopic loops of polymers, macromolecules, or defect lines in complex materials is a challenging task for material scientists. We demonstrate the knotting of microscopic topological defect lines in chiral nematic liquid crystal colloids into knots and links of arbitrary complexity by using l…

Motivated by a question of Rubel, we consider the problem of characterizing which noncompact hypersurfaces in $\RR^n$ can be regular level sets of a harmonic function modulo a $C^\infty$ diffeomorphism, as well as certain generalizations to other PDEs. We prove a versatile sufficient condition that shows, in particular…

We consider the problem of providing nonparametric confidence guarantees for undirected graphs under weak assumptions. In particular, we do not assume sparsity, incoherence or Normality. We allow the dimension $D$ to increase with the sample size $n$. First, we prove lower bounds that show that if we want accurate infe…

Novel bounds improve TD learning consistency in RL.

Paper develops Gaussian approximations and bootstrap for federated LSA with trade-off bounds.

Random forests' performance is analyzed with rates of convergence and asymptotic normality established.

Paper improves CLT and bootstrap approximations for LSA with decreasing step size.

Infinite arms bandit problem solved with confidence bounds.

Cheap methods improve uncertainty in SGD solutions.

Study on financial systems using perturbed unimodal maps with heteroscedastic noise.

New statistical methods improve TD learning for policy evaluation.

The paper improves conformal prediction by analyzing the beta law of conditional coverage.

Study local Weyl law on hyperbolic surfaces, identifying geodesic loops.