arXiv research

Explicit BCH series radii found for special Banach-Malcev shift algebras.

Survey on strong convergence in random matrices and its applications.

Characterizes discontinuous motions of limit sets in quasi-Fuchsian groups.

The study analyzes the convergence rates of Gaussian mixtures of experts.

We characterize sequences of Kleinian surface groups with convergent subsequences in terms of the asymptotic behavior of the ending invariants of the associated hyperbolic 3-manifolds. Asymptotic behavior of end invariants in a convergent sequence predicts the parabolic locus of the algebraic limit as well as how the a…

Similarity algebra extends algebraic structures with quantitative bounds.

Troels Jorgensen conjectured that the algebraic and geometric limits of an algebraically convergent sequence of isomorphic Kleinian groups agree if there are no new parabolics in the algebraic limit. We prove that this conjecture holds in 'most' cases. In particular, we show that it holds when the domain of discontinui…

In this paper, we prove that the $L^4$-norm of Ricci curvature is uniformly bounded along a Kähler-Ricci flow on any minimal algebraic manifold. As an application, we show that on any minimal algebraic manifold $M$ of general type and with dimension $n\le 3$, any solution of the normalized Kähler-Ricci flow converges t…

We show that on Kahler manifolds with negative first Chern class, the sequence of algebraic metrics introduced by H. Tsuji converges uniformly to the Kahler-Einstein metric. For algebraic surfaces of general type and orbifolds with isolated singularities, we prove a convergence result for a modified version of Tsuji's …

Study of pluriclosed flow on Oeljeklaus-Toma manifolds, showing convergence to a soliton.

Functor connects Lie groupoid algebras to bornological structures.

We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the existing optimization-based approach, we work from a purely matrix-algebraic perspective. Moreover, we prove that the algorithm converges locally and exhibits a linear…

The paper discusses methods to compute Green's function on algebraic surfaces using Schottky uniformization.

Study shows a specific Carnot group violates a curvature exponent bound.

Accelerated Gibbs sampling for Gaussian graphical models using dual factor graphs.

The paper studies algebraic integer relations and sequences converging to 4.

The abstract discusses convergence properties of Lipschitz functions and sets defined by equations.

We show that for a strongly convergent sequence of purely loxodromic finitely generated Kleinian groups with incompressible ends, Cannon-Thurston maps, viewed as maps from a fixed base limit set to the Riemann sphere, converge uniformly. For algebraically convergent sequences we show that there exist examples where eve…

We study in this paper three natural notions of convergence of homogeneous manifolds, namely infinitesimal, local and pointed, and their relationship with a fourth one, which only takes into account the underlying algebraic structure of the homogeneous manifold and is indeed much more tractable. Along the way, we intro…

New framework for neural networks converging to low loss without overparameterization.

We show that for a strongly convergent sequence of geometrically finite Kleinian groups with geometrically finite limit, the Cannon-Thurston maps of limit sets converge uniformly. If however the algebraic and geometric limits differ, as in the well known examples due to Kerckhoff and Thurston, then provided the geometr…

The paper explores rigidity and proximality in dynamical systems, proving new results about $C^*$-algebras.

Graph neural networks improve AMG convergence for sparse systems.

We construct a spectral sequence that converges to the cohomology of the chiral de Rham complex over a Calabi-Yau hypersurface and whose first term is a vertex algebra closely related to the Landau-Ginburg orbifold. As an application, we prove an explicit orbifold formula for the elliptic genus of Calabi-Yau hypersurfa…

Proves that emergent algebras right-distributivity implies left-distributivity.

We study the behavior under Gromov-Hausdorff convergence of the spectrum of weighted $\barpartial$-Laplacian on compact Kähler manifolds. This situation typically occurs for a sequence of Fano manifolds with anticanonical Kähler class. We apply it to show that, if an almost smooth Fano-Ricci limit space admits a Kähler…

Anderson and Canary have shown that if the algebraic limit of a sequence of discrete, faithful representations of a finitely generated group into PSL(2,C) does not contain parabolics, then it is also the sequence's geometric limit. We construct examples that demonstrate the failure of this theorem for certain sequences…

Study of curvature flow on complex Lie groups, leading to soliton convergence.

Study on complex curves in hypercomplex nilmanifolds with quaternionic-solvable Lie algebras.

In this paper we use continuous family of multisections of the moduli space of pseudo holomorphic discs to partially improve, in the case of real coefficient, the construction of Lagrangian Floer cohomology of which the author developed jointly with Oh-Ohta-Ono. Namely we associate cyclically symmetric filtered A infin…

In this paper, we will determine the topological types of hyperbolic 3-anifolds H^3/G such that G is a geometric limit of any algebraically convergent sequence of quasi-Fuchsian groups.

New algorithms accelerate value function convergence in MDPs.

We show that the Kahler-Ricci flow on an algebraic manifold of positive Kodaira dimension and semi-ample canonical line bundle converges to a unique canonical metric on its canonical model. It is also shown that there exists a canonical measure of analytic Zariski decomposition on an algebraic manifold of positive Koda…

Paper accelerates MM algorithm for faster inference of ranking scores from comparison data.

The paper uses quaternions to model quantum learning on devices.

Invites probabilistic approach to Kähler-Einstein metrics via random point processes.

Constructs index for elliptic operators using rapidly decaying kernels.

Just as the Temperley-Lieb algebra is a good place to compute the Jones polynomial, the Kauffman bracket skein algebra of a disk with $2k$ colored points on the boundary, each with color $n$, is a good place to compute the $n^{th}$ colored Jones polynomial. Here, this colored skein algebra is shown to be a cellular alg…

New spectral sequence connects link homology to Hochschild homology.

We use the bracket flow/algebraic soliton approach to study the Laplacian flow of $G_2$-structures and its solitons in the homogeneous case. We prove that any homogeneous Laplacian soliton is equivalent to a semi-algebraic soliton (i.e.\ a $G$-invariant $G_2$-structure on a homogeneous space $G/K$ that flows by pull-ba…

New spectral theory for non-associative algebras with applications to Moufang dynamics.

New method uses reinforcement learning to sample from complex data structures efficiently.

Given a compact Kaehler manifold, we consider the complement U of a divisor with normal crossings and a unitary local system V on it. We consider a differential graded Lie algebra (DGLA) of forms with holomorphic logarithmic singularities and vanishing residues. We construct a spectral sequence corresponding to the ant…

The paper examines convergence of distances in Lipschitz structures on manifolds.

The paper explores deep learning through algebra and geometry, highlighting geometric structures and differential processes.

We prove short time existence and uniqueness of the Laplacian flow starting at an arbitrary closed $G_2$-structure. We establish long time existence and convergence of the Laplacian flow starting near a torsion-free $G_2$-structure. We analyze the limit map of the Laplacian flow in relation to the moduli space of torsi…

Given a free group $F_n$, a fully irreducible automorphism $f \in \aut$, and a generic element $x \in F_n$, the elements $f^k(x)$ converge in the appropriate sense to an object called an attracting lamination of $f$. When the action of $f$ on $\frac{F_n}{[F_n, F_n]}$ has finite order, we introduce a homological version…

Kähler-Ricci flow converges on specific toric bundles to solitons.