arXiv research

We calculate the free energy of Coulomb gas systems on Riemann surfaces.

We study the non-asymptotic behavior of a Coulomb gas on a compact Riemannian manifold. This gas is a symmetric n-particle Gibbs measure associated to the two-body interaction energy given by the Green function. We encode such a particle system by using an empirical measure. Our main result is a concentration inequalit…

Quantized Coulomb branches linked to skein algebras.

We study quantized Coulomb branches of quiver gauge theories of Jordan type. We prove that the quantized Coulomb branch is isomorphic to the spherical graded Cherednik algebra in the unframed case, and is isomorphic to the spherical cyclotomic rational Cherednik algebra in the framed case. We also prove that the quanti…

Study of Hilbert schemes and Coulomb branches of hypertoric varieties.

Method identifies causal interactions between time series using extreme eigenvalue variability.

Study quantized SL2-character variety of a once-punctured torus, finding three Coulomb branch isomorphisms.

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.

This is an introduction to a provisional mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ supersymmetric gauge theories, studied in arXiv:1503.03676, arXiv:1601.03586

Proposes a Coulomb-like model for international trade flows, fitting real-world data.

Generative adversarial networks (GANs) evolved into one of the most successful unsupervised techniques for generating realistic images. Even though it has recently been shown that GAN training converges, GAN models often end up in local Nash equilibria that are associated with mode collapse or otherwise fail to model t…

Consider the $3$-dimensional $\mathcal N=4$ supersymmetric gauge theory associated with a compact Lie group $G_c$ and its quaternionic representation $\mathbf M$. Physicists study its Coulomb branch, which is a noncompact hyper-Kähler manifold with an $\mathrm{SU}(2)$-action, possibly with singularities. We give a math…

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

New method uses Coulomb gases for Monte Carlo integration with reduced errors.

The paper connects $G_2$-manifolds to Coulomb and Higgs phases of gauge theories.

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 ${\mathbb C}P^1$ 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.

This is an introduction to a provisional mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ supersymmetric gauge theories, studied in arXiv:1503.03676, arXiv:1601.03586. This is an expanded version of an article arXiv:1612.09014 appeared in the 61st DAISUUGAKU symposium proceeding (2016), wri…

This is the third companion paper of arXiv:1601.03586. When a gauge theory has a flavor symmetry group, we construct a partial resolution of the Coulomb branch as a variant of the definition. We identify the partial resolution with a partial resolution of a generalized slice in the affine Grassmannian, Hilbert scheme o…

We introduce a novel class of localized atomic environment representations, based upon the Coulomb matrix. By combining these functions with the Gaussian approximation potential approach, we present LC-GAP, a new system for generating atomic potentials through machine learning (ML). Tests on the QM7, QM7b and GDB9 biom…

This paper presents the R package GAS for the analysis of time series under the Generalized Autoregressive Score (GAS) framework of Creal et al. (2013) and Harvey (2013). The distinctive feature of the GAS approach is the use of the score function as the driver of time-variation in the parameters of nonlinear models. T…

New gauge condition fixes $L^2$ metric divergence in hyperbolic monopole spaces.

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…

Smooth Yang-Mills fields proved in supercritical dimensions.

GAS models have been recently proposed in time-series econometrics as valuable tools for signal extraction and prediction. This paper details how financial risk managers can use GAS models for Value-at-Risk (VaR) prediction using the novel GAS package for R. Details and code snippets for prediction, comparison and back…

Study analyzes low-energy behavior of Schrödinger operators with Coulomb potentials.

For a given real generic curve $\ga: S^1\to \Bbb {RP}^n$ let $D_\ga$ denote the ruled hypersurface in $\Bbb {RP}^n$ consisting of all osculating subspaces to $\ga$ of codimension 2. A curve $\ga: S^1\to \Bbb {RP}^n$ is called convex if the total number of its intersection points (counted with multiplicities) with any h…

New theorems in 2D and 4D for metrics with curvature or singularity.

Consider the $3$-dimensional $\mathcal N=4$ supersymmetric gauge theory associated with a compact Lie group $G$ and its quaternionic representation $\mathbf M$. Physicists study its Coulomb branch, which is a noncompact hyper-Kähler manifold, such as instanton moduli spaces on $\mathbb R^4$, $SU(2)$-monopole moduli spa…

Extends Coulomb gauge existence to non-associative gauge theory.

The study shows how to regularize weakly harmonic maps using Sobolev norms and Coulomb frames.

Study on Wasserstein gradient flow for MMD between Coulomb measures.

This is a supplement to [arXiv:1503.03676], where an approach towards a mathematically rigorous definition of the Coulomb branch of a $3$-dimensional $\mathcal N=4$ 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.

This paper analyzes Ethereum's gas fees and their derivatives, providing a comprehensive model.

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…

Geodesic X-ray transform proves injective for smooth one-forms on gas giant manifolds.

Study the Hessian geometry of an ideal gas in a centrifuge.

Monoidal categorifies genus zero skein algebra using K-theory.

The prediction of the gas production from mature gas wells, due to their complex end-of-life behavior, is challenging and crucial for operational decision making. In this paper, we apply a modified deep LSTM model for prediction of the gas flow rates in mature gas wells, including the uncertainties in input parameters.…

Introduces GA-P/E, a growth-adjusted stock valuation measure.

Improved GAS models using trees and forests for better forecasts.

This study compares GNNs and GA-MLPs, finding GA-MLPs can distinguish graphs but not count walks.

This is the second companion paper of arXiv:1601.03586. We consider the morphism from the variety of triples introduced in arXiv:1601.03586 to the affine Grassmannian. The direct image of the dualizing complex is a ring object in the equivariant derived category on the affine Grassmannian (equivariant derived Satake ca…

Paper proposes GAS-ALD model for financial risk prediction.

Let $A$ be a $W^{1,2}$-connection on a principle $\text{SU}(2)$-bundle $P$ over a compact $4$-manifold $M$ whose curvature $F_A$ satisfies $\|F_A\|_{L^2(M)}\le Λ$. Our main result is the existence of a global section $σ: M\to P$ with finite singularities on $M$ such that the connection form $σ^*A$ satisfies the Coulomb…

Optimizes routing in decentralized exchanges with gas fees.