arXiv research

Improved Kuznecov remainder estimates for generic metrics.

Study eta invariant remainder on contact manifolds, improving previous results.

Improved estimate for remainder term in Weyl law for congruence subgroups of Chevalley groups.

A new systolic inequality with a remainder for the real projective plane.

We investigate the remainder in the asymptotic formula for the number of integer points in a family of bounded domains in the Euclidean space, which remain unchanged along some linear subspace and expand in the directions, orthogonal to this subspace. We prove some estimates for the remainder, imposing additional assum…

Improved remainder estimate for eigenvalue asymptotics on manifolds with group actions.

We obtain an estimate from below for the remainder in Weyl's law on negatively curved surfaces. In the constant curvature case, such a bound was proved independently by Hejhal and Randol in 1976 using the Selberg zeta function techniques. Our approach works in arbitrary negative curvature, and is based on wave trace as…

Paper introduces statistical CRT for robust multiple parameter estimation.

We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl's law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the D…

Proves a lower bound for Θ function on manifolds without conjugate points.

We derive an Ehrhart function for symbols from the Euler-MacLaurin formula with remainder.

Paper sharpens Hardy and Rellich inequalities on nonreversible Finsler manifolds.

The paper describes spectra of operators on rational homogeneous varieties.

Study heat traces for drifting Laplacian and Schrödinger operators on manifolds.

Let $Ω$ be a bounded domain with $C^\infty$ boundary in an $n$-dimensional $C^\infty$ Riemannian manifold, and let $\varrho$ be a non-negative bounded function defined on $\partial Ω$. It is well-known that for the biharmonic equation $Δ^2 u=0$ in $Ω$ with the 0-Dirichlet boundary condition, there exists an infinite se…

Simple knots in lens spaces fiber if their order doesn't divide certain Euclidean remainders.

We prove an asymptotic formula for the number of integer points in a family of bounded domains in the Euclidean space with smooth boundary, which remain unchanged along some linear subspace and stretch out in the directions, orthogonal to this subspace. A more precise estimate for the remainder is obtained in the case …

Let (M, g) be a compact smooth Riemannian manifold. We obtain new off-diagonal estimates as λ tend to infinity for the remainder in the pointwise Weyl Law for the kernel of the spectral projector of the Laplacian onto functions with frequency at most λ. A corollary is that, when rescaled around a non self-focal point, …

We give a purely complex geometric proof of the existence of the Bergman kernel expansion. Our method provides a sharper estimate, and in the case that the metrics are real analytic, we prove that the remainder decays faster than any polynomial.

Simple quantile regression method wins GEFCom2017 probabilistic load forecasting competition.

Paper proves convergence of MDL to Einstein-Hilbert with boundary term.

Study embeddings between Barron spaces with various activation functions, focusing on RePU.

New insights connect strong coupling SYM amplitudes to hyperkähler geometry.

Proves estimates for Calabi-Yau metrics as Kahler classes shrink.

New exact Taylor series for PDEs solutions.

Optimal portfolio selection in incomplete markets analyzed with SPDEs and HJB equations.

The study reveals scaling limits of spectral projectors on Riemannian manifolds.

Let $(M, {g})$ be a compact, $d$-dimensional Riemannian manifold without boundary. Suppose further that $(M,g)$ is either two dimensional and has no conjugate points or $(M,g)$ has non-positive sectional curvature. The goal of this note is to show that the long time parametrix obtained for such manifolds by Bérard can …

Study links Hopf differentials to curvature line flows on time-like CMC surfaces.

We introduce a fractional Yamabe flow involving nonlocal conformally invariant operators on the conformal infinity of asymptotically hyperbolic manifolds, and show that on the conformal spheres $(\Sn, [g_{\Sn}])$, it converges to the standard sphere up to a Möbius diffeomorphism. This result allows us to obtain extinct…

The paper proves a Bonnesen-type inequality for the real projective plane.

Researchers extend asymptotic analysis to Bergman projections with Gevrey weights.

Defines spectral sequences for fiberwise Dirac operators and proves adiabatic limit formula.

Proposes a method to learn policies from offline data with reduced bias.

This paper analyzes quantiles of heavy-tailed distributions, separating projection direction and quantile threshold effects.

In this paper we study minimal and constant mean curvature (cmc) periodic surfaces in H^2 x R. More precisely, we consider quotients of H^2 x R by discrete groups of isometries generated by horizontal hyperbolic translations f and/or a vertical translation T. In the quotient by the Z^2 subgroup of the isometry group ge…

Solutions near infinity to special Lagrangian equations are asymptotic to quadratic polynomials with logarithmic terms.

Study on the formation of singularities in mean curvature flow.

RPN unifies various models with a reconciled polynomial network.

The paper explores how dynamic preconditioning affects the CLT in online averaging.

We study the free energy of the Laughlin state on curved backgrounds, starting from the free field representation. A simple argument, based on the computation of the gravitational effective action from the transformation properties of Green functions under the change of the metric, allows to compute the first three ter…

ADIGen: Automatic, Debiased, and Invariant Counterfactual Generation

Algorithm for decentralized competition among adaptive agents.

Algorithm learns principal curves from data streams in a sequential manner.

Let p be an odd regular prime, and assume that the Lichtenbaum-Quillen conjecture holds for K(Z[1/p]) at p. Then the p-primary homotopy type of the smooth Whitehead spectrum Wh(*) is described. A suspended copy of the cokernel-of-J spectrum splits off, and the torsion homotopy of the remainder equals the torsion homoto…

New framework improves neural network robustness without sacrificing accuracy.

New method bounds high-dimensional regression without estimating design covariance.

The paper proves inequalities for closed surfaces involving mean curvature.