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.
Classifies geodesic-preserving bijections in Thurston geometries.
Convexity properties are preserved under radial transformations in hyperbolic and spherical geometries.
Spectral graph sparsification preserves geometry of GNN embeddings.
We address the problem of local geometry of third order ODEs modulo contact, point and fibre-preserving transformations of variables. Several new and already known geometries are described in a uniform manner by the Cartan method of equivalence. This includes conformal, Weyl and metric geometries in three and six dimen…
The paper examines flows that preserve area and length in hyperbolic geometry.
New saddle network architectures preserve convex-concave geometry in optimization problems.
Dual pairs constructed for volume preserving diffeomorphisms using symplectic geometry.
Here, by extending the definition of circle to Finsler geometry, we show that, every circle-preserving local diffeomorphism is conformal. This result implies that in Finsler geometry, the definition of concircular change of metrics, a priori, does not require the conformal assumption.
Geometric framework for SPD matrices preserving subspace structures.
This paper attempts to define a generalisation of the standard Einstein condition (in conformal/metric geometry) to any parabolic geometry. To do so, it shows that any preserved involution of the adjoint bundle $\mc{A}$ gives rise, given certain algebraic conditions, to a unique preferred affine connection …
The paper characterizes measures preserving independence through planar web geometry.
A new curve flow preserves area and converges to a circle.
Unified theory of measure-preserving diffusions on manifolds.
Paper proposes a new method for supervised manifold learning using random forest proximities.
A PhD thesis written under supervision of Pawel Nurowski and defended at the Faculty of Physics of the University of Warsaw. We adress the problems of local equivalence and geometry of third order ODEs modulo contact, point and fibre-preserving transformations of variables. Several new and already known geometries are …
Classifies nets with area-preserving transformations into two types.
CoreFlow models matrix-valued distributions efficiently, preserving shared low-rank structure.
New formulation of Schrödinger connections preserves vector lengths in geometry.
Proof confirms preservation of projective limits in synthetic differential geometry.
A new geometry-preserving method for interpreting compositional data.
We show that the supersymmetric near horizon black hole geometries of 6-dimensional supergravity coupled to any number of scalar and tensor multiplets are either locally , where Σ^3 is a homology 3-sphere, or $\bR^{1,1}\times {\cal S}^4$, where is a 4-manifold whose geometry depends on the…
Sharp 3D Alexandrov inequality applied to volume-preserving flows.
The Blum medial axis rigidity is studied in terms of cross ratios and differential geometry.
New results on geometry of area-preserving diffeomorphisms using braids.
Asymmetric expansion preserves convexity in hyperbolic geometry.
Heterotic backgrounds described using generalised geometry, preserving minimal supersymmetry.
In this paper we study geometry of symmetric torsion-free connections which preserve a given symplectic form
The group of area preserving diffeomorphisms showed importance in the problems of self-dual gravity and integrability theory. We discuss how representations of this infinite-dimensional Lie group can arise in mathematical physics from pure local considerations. Then using Lie algebra extensions and cohomology we derive…
Study variations of metrics on Riemannian submersions to preserve fiber geometry.
Pachner move 3 ->3 deals with triangulations of four-dimensional manifolds. We present an algebraic relation corresponding in a natural way to this move and based, a bit paradoxically, on three-dimensional geometry.
We systematically analyse the necessary and sufficient conditions for the preservation of supersymmetry for bosonic geometries of the form R^{1,9-d} \times M_d, in the common NS-NS sector of type II string theory and also type I/heterotic string theory. The results are phrased in terms of the intrinsic torsion of G-str…
Lie contact structures generalize the classical Lie sphere geometry of oriented hyperspheres in the standard sphere. They can be equivalently described as parabolic geometries corresponding to the contact grading of orthogonal real Lie algebra. It follows the underlying geometric structure can be interpreted in several…
Improved random forest proximities capture data geometry.
Introduces new deformation classes in generalized Kähler geometry.
We consider the problem of efficient randomized dimensionality reduction with norm-preservation guarantees. Specifically we prove data-dependent Johnson-Lindenstrauss-type geometry preservation guarantees for Ho's random subspace method: When data satisfy a mild regularity condition -- the extent of which can be estima…
We classify submersions from to up to diffeomorphisms which preserve the swallowtail and use this classification to study its flat geometry. The flat geometry is derived from the contact of the swallowtail with planes, which is measured by the singularities of the height function.
We prove an existence result for local and global G-structure preserving affine immersions between affine manifolds. Several examples are discussed in the context of Riemannian and semi-Riemannian geometry, including the case of isometric immersions into Lie groups endowed with a left-invariant metric, and the case of …
We study non-degenerate CR geometries of hypersurface type that are symmetric in the sense that, at each point, there is a CR transformation reversing the CR distribution at that point. We show that such geometries are either flat or homogeneous. We show that non-flat non-degenerate symmetric CR geometries of hypersurf…
Bi-Lipschitz Autoencoder ensures robust manifold preservation.
For a germ of a smooth map f and a subgroup G_V of any of the Mather groups G for which the source or target diffeomorphisms preserve some given volume form V in the source or in the target we study the G_V-moduli space of f that parameterizes the G_V-orbits inside the G-orbit of f. We find, for example, that this modu…
We study the Riemannian geometry of 3D axisymmetric ideal fluids. We prove that the exponential map on the group of volume-preserving diffeomorphisms of a -manifold is Fredholm along axisymmetric flows with sufficiently small swirl. Along the way, we define the notions of axisymmetric and swirl-free diffeomorp…
We introduce a notion of moment map adapted to actions of Lie groups that preserve a closed three-form. We show existence of our multi-moment maps in many circumstances, including mild topological assumptions on the underlying manifold. Such maps are also shown to exist for all groups whose second and third Lie algebra…
Logarithmic connections on complex manifolds with trivial tangent bundle.
Revises Gauss's Lemma using metrical distortion and differential slip.
We prove a theorem relating the automorphism group of a Cartan geometry to the group on which the geometry is modeled: a component of the adjoint representation of the first embeds in the adjoint representation of the second. Consequences of the theorem include general bounds on the rank and nilpotence degree of an aut…
New approach uses isotropic geometry to solve Euclidean problems.
DMT enhances deep neural networks to better preserve data structures.
Kähler-Ricci flow preserves negative anti-bisectional curvature.