arXiv research

Study of Calabi-Yau manifold degenerations near complex structure limits.

The study finds many tight contact structures on hyperbolic 3-spheres.

We endow projective (resp. direct) limits of Banach tensor structures with Fréchet (resp. convenient) structures and study adapted connections to $G$-structures in both frameworks. This situation is illustrated by a lot of examples.

This research connects Higgs bundles to projective structures via conformal limits.

We equip the direct limit of tangent bundles of paracompact finite dimensional manifolds with a structure of convenient vector bundle with structural group $GL(\infty,\mathbb{R}) =\underrightarrow{\lim}GL(\mathbb{R}^{n})$.

The study proves compactness and structure of Ricci flow limits.

Study of conformal limits for special opers in Lie groups.

The paper extends Nambu-Poisson structures to infinite dimensions.

We study the limits of holonomy representations of complex projective structures on a compact Riemann surface in the Morgan-Shalen compactification of the character variety. We show that the dual R-trees of the quadratic differentials associated to a divergent sequence of projective structures determine the Morgan-Shal…

We study some similarities between almost product Riemannian structures and almost Hermitian structures. Inspired by the similarities, we prove lower eigenvalue estimates for the Dirac operator on compact Riemannian spin manifolds with locally product structures. We also provide some examples (limiting manifolds) for t…

Given a sequence of complete(compact or noncompact) Kähler manifolds $M^n_i$ with bisectional curvature lower bound and noncollapsed volume, we prove that the pointed Gromov-Hausdorff limit is homeomorphic to a normal complex analytic space. The complex analytic structure is the natural "limit" of complex structure of …

Extends Dirac structures to infinite dimensions, focusing on convenient Lie algebroids and manifolds.

Survey on Nambu-Poisson structures in infinite dimensions.

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

We define the notion of strong projective limit of Banach Lie algebroids. We study the associated structures of Fréchet bundles and the compatibility with the different morphisms. This kind of structure seems to be a convenient framework for various situations.

The study connects K-stability and large complex structure limits in mirror symmetry.

We discuss the Euclidean limit of hyperbolic SU(2)-monopoles, framed at infinity, from the point of view of pluricomplex geometry. More generally, we discuss the geometry of hypercomplex manifolds arising as limits of pluricomplex manifolds.

We explore the plane-wave limit of homogeneous spacetimes. For plane-wave limits along homogeneous geodesics the limit is known to be homogeneous and we exhibit the limiting metric in terms of Lie algebraic data. This simplifies many calculations and we illustrate this with several examples. We also investigate the beh…

In this paper, we explore the limit structure of a sequence of Riemannian manifolds with Bakry-Émery Ricci curvature bounded below in the Gromov-Hausdorff topology. By extending the techniques established by Cheeger-Cloding for Riemannian manifolds with Ricci curvature bounded below, we prove that each tangent space at…

We construct a geometric structure on deformed supermanifolds as a certain subalgebra of the vector fields. In the classical limit we obtain a decoupling of the infinitesimal odd and even transformations, whereas in the semiclassical limit the result is a representation of the supersymmetry algebra. In the case of mass…

We investigate variations of Brieskorn lattices over non-compact parameter spaces, and discuss the corresponding limit objects on the boundary divisor. We study the associated variation of twistors and the corresponding limit mixed twistor structures. We construct a compact classifying space for regular singular Briesk…

Paper explores limits of exact inference in structured prediction models.

A geometric transition is a continuous path of geometric structures that changes type, meaning that the model geometry, i.e. the homogeneous space on which the structures are modeled, abruptly changes. In order to rigorously study transitions, one must define a notion of geometric limit at the level of homogeneous spac…

Scientific fields such as insider-threat detection and highway-safety planning often lack sufficient amounts of time-series data to estimate statistical models for the purpose of scientific discovery. Moreover, the available limited data are quite noisy. This presents a major challenge when estimating time-series model…

In this paper, we study the information-theoretic limits of learning the structure of Bayesian networks (BNs), on discrete as well as continuous random variables, from a finite number of samples. We show that the minimum number of samples required by any procedure to recover the correct structure grows as $Ω(m)$ and $Ω…

In this paper, we study the structure of the limit space of a sequence of almost Einstein manifolds, which are generalizations of Einstein manifolds. Roughly speaking, such manifolds are the initial manifolds of some normalized Ricci flows whose scalar curvatures are almost constants over space-time in the $L^1$-sense,…

We prove that direct limits of finite dimensional Lie algebroids and their prolongations can be endowed with structures of convenient spaces.

The paper proves mirror symmetry for del Pezzo surfaces and computes related structures.

The aim of the paper is to investigate the relation between inverse limit of branched manifolds and codimension zero laminations. We give necessary and sufficient conditions for such an inverse limit to be a lamination. We also show that codimension zero laminations are inverse limits of branched manifolds. The inverse…

The paper examines sequences of metric spaces converging to compact limits with specific properties.

We study the limit set of discrete subgroups arising from Anosov representations. Specially we study the limit set of discrete groups arising from strictly convex real projective structures and Anosov representations from a finitely generated word hyperbolic group into a semisimple Lie group.

Extends arguments to limit structure in Calabi-Yau degenerations.

Limits of manifolds with Kato bound on Ricci curvature are rectifiable.

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…

Study shows colored Jones invariants limit to link volumes.

Theoretical limits of deep residual networks show consistent covariance structures.

Study of limiting configurations for SU(1,2) Hitchin equation solutions.

Global graph structure improves GNN performance.

New framework captures non-autonomous IFS limit set topology.

Researchers examine various causal structures for spacetimes with continuous metrics.

The paper proves a conjecture about manifold limits and characterizes their structure.

The study defines a canonical nilpotent structure for certain collapsed manifolds.

Constructs tri-Hamiltonian structure and Frobenius manifold for asymmetric gAL hierarchy

CSTS benchmarks time series clustering by evaluating correlation structures.

Study geometric structure of Ricci shrinker ends without global curvature assumptions.

Kaehler-Einstein metrics on orbifolds derived from Einstein sequences.

Caratheodory's axiom limits arbitrage in resource-limited systems.

Paper bridges quantum and classical mechanics for open systems.