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.
Survey explores cohomology's roles in applied math and sciences.
Determines algebra structure of complex differential forms operators.
Proves a theorem for complex flat vector bundles using differential forms.
We obtain a new differentiable sphere theorem for compact Lagrangian submanifolds in complex Euclidean space and complex projective space.
The paper constructs Levi flat structures using structure sheaves and differential complexes.
The paper uses complex-valued functions to simplify plane differential geometry and kinematics.
Advances M-polyfolds for complex geometry applications.
This paper defines and examines the basic properties of noncommutative analogues of almost complex structures, integrable almost complex structures, holomorphic curvature, cohomology, and holomorphic sheaves. The starting point is a differential structure on a noncommutative algebra defined in terms of a differential g…
Quantum complexity lowerbound proved using differential geometry.
In these expository notes we draw together and develop the ideas behind some recent progress in two directions: the treatment of finite type partial differential operators by prolongation, and a class of differential complexes known as detour complexes. This elaborates on a lecture given at the IMA Summer Programme ``S…
Article proves tangent complex structure of Lie n-groupoid.
Smooth complex surfaces with triple intersections using differential geometry.
We construct a versal family of deformations of CR structures in five dimensions, using a differential complex closely related to the differential form complex introduced by Rumin for contact manifolds.
Reformulates elasticity complex with new differential and Hodge star operators.
Survey of geometry developments, including complex structures on surfaces.
We study two notions of relative differential cohomology, using the model of differential characters. The two notions arise from the two options to construct relative homology, either by cycles of a quotient complex or of a mapping cone complex. We discuss the relation of the two notions of relative differential cohomo…
The paper extends statistical estimation techniques under differential privacy.
New Spencer complexes for Lie groupoids developed.
Differentiable ABMs face challenges in inference and optimisation.
In this paper, we introduce a new concept so called harmonic complex structure by using harmonic theory for vector bundle-valued differential forms. It is a new structure intermediates between complex structure and Kähler structure. From differential geometric viewpoint, it is a natural generalization of Kähler structu…
Introduces differential forms to study inequalities between eigenvalues.
The study characterizes complex structures using calculus of variations.
For a symplectic manifold admitting a metaplectic structure and for a Kuiper map, we construct a complex of differential operators acting on exterior differential forms with values in the dual of the Kostant's symplectic spinor bundle. Defining a Hilbert -structure on this bundle for a suitable -algebra, we o…
Study on opers over complex manifolds of dimension one.
The study characterizes a complex curve of residueless meromorphic differentials on elliptic curves.
In this note, we report the back propagation formula for complex valued singular value decompositions (SVD). This formula is an important ingredient for a complete automatic differentiation(AD) infrastructure in terms of complex numbers, and it is also the key to understand and utilize AD in tensor networks.
This paper classifies components of meromorphic differential strata.
New operators generalize Michelsohn's on almost Hermitian manifolds.
PINNs solve differential geometry problems in complex shapes.
This article provides a complete description of the differential Gerstenhaber algebras of all nilpotent complex structures on any real six-dimensional nilpotent algebra. As an application, we classify all pseudo-Kählerian complex structures on six-dimensional nilpotent algebras such that the differential Gerstenhaber a…
We use the Grauert--Grothendieck complex on differentiable spaces to study basic relative forms on the inertia space of a compact Lie group action on a manifold. We prove that the sheaf complex of basic relative forms on the inertia space is a fine resolution of Bryliski's sheaf of functions on the inertia space.
The study sets limits on the complexity of Klein geometries.
We study variuos homological structures associated with Poisson algebra, the canonical differential complex for singular Poisson structure and the analogue of the star operator for such manifolds. Give the interpretation of the classical Koszul differential of exterior forms, as the supercommutator with some second ord…
Study differentiable maps on hypersurface links, finding fold maps with circle singular value sets.
On a symplectic manifold, there is a natural elliptic complex replacing the de Rham complex. It can be coupled to a vector bundle with connection and, when the curvature of this connection is constrained to be a multiple of the symplectic form, we find a new complex. In particular, on complex projective space with its …
Diffeology extends differential geometry to complex spaces.
Given a generic Lagrangian system, its Euler-Lagrange operator obeys Noether identities which need not be independent, but satisfy first-stage Noether identities, and so on. This construction is generalized to arbitrary differential operators on a smooth fiber bundle. Namely, if a certain necessary and sufficient condi…
Lecture notes on BGG complexes using Lie groups and algebras.
The paper proves isomorphisms between two complexes related to singular foliations.
We give a necessary and sufficient condition for a non-degenerate symmetric 3-differential with nonzero Blaschke curvature on a complex surface to be locally representable as a product of three closed holomorphic 1-forms. We give two versions of this condition corresponding to different choices of coordinates, one of w…
Study on complex line fields on almost-complex manifolds, proving existence conditions.
New complexes refine multicomplexes for subRiemannian geometry.
A meromorphic quadratic differential with poles of order two, on a compact Riemann surface, induces a measured foliation on the surface, with a spiralling structure at any pole that is determined by the complex residue of the differential at the pole. We introduce the space of such measured foliations, and prove that f…
This paper deals with the notion of quadratic differential in spherical CR geometry (or more generally on strictly pseudoconvex CR manifolds). We get to this notion by studying a splitting of Rumin complex and discuss its first features such as trajectories and length. We also define several differential operators on q…
Study differentially private methods for learning Hawkes processes.
Poincar{é} and Sobolev inequalities for differential forms on Heisenberg balls, involving Rumin's differentials, are given. Furthermore, a global homotopy of Rumin's complex which improves differentiability of Rumin forms is provided on any bounded geometry contact manifold.
Study of -eigenvalues for complex tensors and their applications in differential geometry.
Neural differential equations combine deep learning and differential equations for modeling complex systems.