A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Defines simplicity of non-linear mappings using information geometry.
New complex-valued maps found on complex geometries.
Elliptic theory explains indicial weights for non-linear geometry problems.
Develops a Riemannian archetypal analysis for interpretable non-linear data.
Paper studies solutions to a specific equation in conformal geometry with singular sets.
Extends parabolic study to flat hyperkähler manifolds.
This work develops methods to analyze data on curved spaces using deep learning.
Study of nonlinear PDEs using derived geometry and BV formalism.
New solutions found for complex-valued harmonic morphisms with rational exponents.
Non linear sigma models are quantum field theories describing, in the large deviations sense, random fluctuations of harmonic maps between a Riemann surface and a Riemannian manifold. Via their formal renormalization group analysis, they provide a framework for possible generalizations of the Hamilton-Perelman Ricci fl…
Derives estimates for geometric elliptic equations on complex manifolds.
Exposes graded and microformal geometry, focusing on -manifolds.
Veronese webs are rich geometric structures with deep relationships to various domains of mathematics. The PDEs which determine the Veronese web are overdetermined if dim >3, but in the case dim =3 they reduce to a special flavor of a non-linear wave equation. The symmetries embedded in the definition of a Veronese web…
Reviews uses of nonlinear sigma models in various systems.
Surveying inverse problems on manifolds with boundaries.
New solutions found using rational exponents in complex-valued geometry.
Geometry arising from two diffusion operators (smooth semi-elliptic, second order differential operators) on different spaces but intertwined by a smooth map is described. Particular cases arise from Riemannian submersions when the operators are Laplace-Beltrami operators, from equivariant operators on the total space …
Methodology to measure non-linear correlations using copulas and clustering.
This work improves manifold learning for multi-modal data.
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man ifold geometry using either local or global features of the data. Building on t…
New conformal geometry method solves Einstein-Weyl equations.
In the neighborhood of a regular point, generalized Kahler geometry admits a description in terms of a single real function, the generalized Kahler potential. We study the local conditions for a generalized Kahler manifold to be a generalized Calabi-Yau manifold and we derive a non-linear PDE that the generalized Kahle…
Study of geometry of symplectomorphisms on manifolds.
Here, a non-linear analysis method is applied rather than classical one to study projective Finsler geometry. More intuitively, by means of an inequality on Ricci-Finsler curvature, a projectively invariant pseudo-distance is introduced and an analogous of Schwarz' lemma in Finsler geometry is proved. Next, the Schwarz…
Here, a non-linear analysis method is applied rather than classical one to study projective changes of Finsler metrics. More intuitively, a projectively invariant pseudo-distance is introduced and characterized with respect to the Ricci tensor and its covariant derivatives.
We discuss in rather general terms quantum field theories dealing with spaces of maps between Riemannian manifolds. In particular we explore the well--known connection between the renormalization group flow for non--linear sigma models and the Ricci flow.
Defines spectral selectors on lens spaces for contactomorphisms.
In recent years, the study of the interplay between (fully) non-linear potential theory and geometry received important new impulse. The purpose of this work is to move a step further in this direction by investigating appropriate versions of parabolicity and maximum principles at infinity for large classes of non-line…
New theory proves representability of PDE solutions without complex machinery.
To pave the way for the journey from geometry to conformal field theory (CFT), these notes present the background for some basic CFT constructions from Calabi-Yau geometry. Topics include the complex and Kaehler geometry of Calabi-Yau manifolds and their classification in low dimensions. I furthermore discuss CFT const…
New approach connects Finsler geometry's metric and connections.
Geometric Variational Inference improves efficiency in complex probability distributions.
The aim of this paper is to construct a natural Riemann-Lagrange differential geometry on 1-jet spaces, in the sense of nonlinear connections, generalized Cartan connections, d-torsions, d-curvatures, jet electromagnetic fields and jet Yang-Mills energies, starting from some given non-linear evolution DEs systems model…
In this paper we examine the Riemannian geometry of the group of contactomorphisms of a compact contact manifold. We compute the sectional curvature of in the sections containing the Reeb field and show that it is non-negative. We also solve explicitly the Jacobi equation along the geodesic correspon…
We construct a tangent bundle exponential map and locally autoparallel coordinates for geometries based on a general connection on the tangent bundle of a manifold. As concrete application we use these new coordinates for Finslerian geometries and obtain Finslerian geodesic coordinates. They generalise normal coordinat…
Auxiliary equations improve bounds in symplectic geometry.
In this lecture delivered at the Integrable and Quantum Field Theory at Peyresq sixth meeting, we review the Lychagin's Monge-Ampere operators theory and exhibit the link it establishes between the classical problem of local equivalence for non linear partial differential equations and the problem of integrability of s…
Riemannian geometry improves protein dynamics analysis.
Mathematical treatment of sigma model's low energy theory.
Method estimates mixture components without discretizing parameters.
In this communication, complex systems with a near trivial dynamics are addressed. First, under the hypothesis of equiprobability in the asymptotic equilibrium, it is shown that the (hyper) planar geometry of an -dimensional multi-agent economic system implies the exponential (Boltzmann-Gibss) wealth distribution an…
We show that the theory of isothermic surfaces in $\E^3$ -- one of the oldest branches of differential geometry -- can be reformulated within the modern theory of completely integrable (soliton) systems. This enables one to study the geometry of isothermic surfaces in $\E^3$ by means of powerful spectral methods availa…
We develop an approach to construct Poisson algebras for non-linear scalar field theories that is based on the Cahiers topos model for synthetic differential geometry. In this framework the solution space of the field equation carries a natural smooth structure and, following Zuckerman's ideas, we can endow it with a p…
Paper proves uniform continuity bounds for complex Monge-Ampère solutions.
We discuss the conditions for additional supersymmetry and twisted supersymmetry in N = (2, 2) supersymmetric non-linear sigma models described by one left and one right semi-chiral superfield and carrying a pair of non-commuting complex structures. Focus is on linear non-manifest transformations of these fields that h…
Survey of recent geometric flows in complex geometry.
This is a survey paper on several aspects of differential geometry for the last 30 years, especially in those areas related to non-linear analysis. It grew from a talk I gave on the occasion of seventieth anniversary of Chinese Mathematical Society. I dedicate the lecture to the memory of my teacher S.S. Chern who had …
New recursion found for hyperbolic sphere volumes.