arXiv research

The study of logarithmic fields associated with nilmanifolds and their singularities.

Constructs a Hodge filtration for vector fields of complex reflection groups.

The paper finds that circles and logarithmic spirals are the only constant-speed ramps for a specific force field.

The paper analyzes competition among fund managers using excess logarithmic returns and constructs games to find optimal allocations.

In this work, we give a formula for the logarithmic invariant of knots in terms of certain derivatives of the colored Jones invariant. This invariant is related to the logarithmic conformal field theory, and was defined by using the centers in the radical of the restricted quantum group at root of unity. A relation bet…

Study Higgs bundles on curves with punctures, extending spectral correspondence.

The paper constructs a Saito basis for a specific class of divisors and applies it to logarithmic Poisson geometry.

Proves a stack of G-bundles with logarithmic connections is finite type.

The paper provides estimates for flows on Riemannian manifolds using truncated expansions.

Logarithmic connections on principal bundles over normal varieties are studied.

Given for instance a finite volume negatively curved Riemannian manifold $M$, we give a precise relation between the logarithmic growth rates of the excursions into cusps neighborhoods of the strong unstable leaves of negatively recurrent unit vectors of $M$ and their linear divergence rates under the geodesic flow. As…

The paper analyzes Q-learning in 2-player Markov games and provides gap-dependent logarithmic regret bounds.

This work shows linear convergence for two-layer neural networks in mean-field regime.

Improved particle approximation for mean-field neural networks.

We shall introduce the notion of $C^\infty$ logarithmic symplectic structures on a differentiable manifold which is an analog of the one of logarithmic symplectic structures in the holomorphic category. We show that the generalized complex structure induced by a $C^\infty$ logarithmic symplectic structure has unobstruc…

Near-logarithmic regret per switch achieved for mixable/exp-concave losses.

Study on Willmore spheres, calculating their index and relating it to minimal surfaces.

Random Gaussian fields on 4D Riemannian manifolds with conformal invariance.

Proves a Baum--Bott formula for foliations by curves with logarithmic terms.

Paper optimizes approximating high-dimensional diffusions by independent coordinates.

Uniform-in-time analysis for Stein Variational Gradient Descent across various metrics.

The logarithmic Riemann surface Sigma_{log} is a classical holomorphic 1-manifold. It lives into R^4 and induces a covering space of C - 0 defined by exp. This paper suggests a geometric construction of it, derived as the limit of a sequence of vector fields extending exp suitably to embeddings of C into R^3, which tur…

We study the convergence of the Kähler-Ricci flow on a Fano manifold under some stability conditions. More precisely we assume that the first eingenvalue of the $\bar\partial$-operator acting on vector fields is uniformly bounded along the flow, and in addition the Mabuchi energy decays at most logarithmically. We then…

Constructs curves in log-symplectic manifolds, classifying and obstructing certain structures.

In the spirit of the emergent field of econophysics, a goodness-of-fit test for the Power-Law distribution, based on the Empirical Distribution Function (EDF) is presented, and related problems are discussed. An analysis of the tail behaviour of the daily logarithmic variation of the Mexican Stock Market Index (IPC), s…

We adapt a Markov Random Field learning algorithm for continuous variables.

Study geodesic X-ray transforms on curved manifolds using Carleman estimates.

We apply a study of orders in quaternion algebras, to the differential geometry of Riemann surfaces. The least length of a closed geodesic on a hyperbolic surface is called its systole, and denoted syspi_1. P. Buser and P. Sarnak constructed Riemann surfaces X whose systole behaves logarithmically in the genus g(X). Th…

The study finds infinitely many semi-arithmetic Riemann surfaces with dense systoles and distinct invariant trace fields.

In this paper, we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure; we prove that the latter induces a representation by logarithmic derivation of the module of logarithmic Kahler differentials; therefore, it induces a differential complex from which we derive the notio…

New uncertainty principle for Schrödinger equations on hyperbolic manifolds.

Paper studies convergence of Mean-Field GDA dynamics for MNE of continuous games.

The study finds infinite commensurability classes of hyperbolic manifolds with Salem number lengths.

Optimizes variational inference for dynamic network models.

This paper constructs a non-Archimedean Teichmüller space using tropical geometry.

Given a negatively curved geodesic metric space $M$, we study the statistical asymptotic penetration behavior of (locally) geodesic lines of $M$ in small neighborhoods of points, of closed geodesics, and of other compact (locally) convex subsets of $M$. We prove Khintchine-type and logarithme law-type results for the s…

Sharp bounds on heat kernel derivatives on incomplete manifolds.

Let G be a finite group of complex n by n unitary matrices generated by reflections acting on C^n. Let R be the ring of invariant polynomials, and χbe a multiplicative character of G. Let Ω^χbe the R-module of χ-invariant differential forms. We define a multiplication in Ω^χand show that under this multiplication Ω^χha…

Our main result is that for all sufficiently large $x_0>0$, the set of commensurability classes of arithmetic hyperbolic 2- or 3-orbifolds with fixed invariant trace field $k$ and systole bounded below by $x_0$ has density one within the set of all commensurability classes of arithmetic hyperbolic 2- or 3-orbifolds wit…

New method solves $\bar{\partial}$-equations for logarithmic forms on Kahler manifolds.

Study shows polynomial-width neural networks can closely approximate infinite-width networks in polynomial time.

Study rigidity by logarithmic capacity and related functions.

Privacy constraints affect learning Markov Random Fields differently.

We study Bogomolny equations on $R^2\times S^1$. Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions with Higgs field growing logarithmically at infinity. We call these solutions periodic monopoles. Using Nahm transform, we show that periodic monop…

Study excess logarithmic residues for foliations to bound invariant hypersurfaces and test log canonicity.

Study real logarithms of semi-simple matrices, focusing on differential structure.

Introduces logarithmic Cartan geometry on complex manifolds with singularities.

We introduce linear holonomy on Poisson manifolds. The linear holonomy of a Poisson structure generalizes the linearized holonomy on a regular symplectic foliation. However, for singular Poisson structures the linear holonomy is defined for the lifts of tangential path to the cotangent bundle (cotangent paths). The lin…