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 solitons and flows for generalized Ricci flow on nilpotent Lie groups.
Study shows limitations of Lie bracket commutation for nonsmooth vector fields.
A new Poisson bracket defined on Poisson structures with applications to fixed points and cohomology.
In this paper, we study the Ricci flow of solvmanifolds whose Lie algebra has an abelian ideal of codimension one, by using the bracket flow. We prove that solutions to the Ricci flow are immortal, the omega-limit of bracket flow solutions is a single point, and that for any sequence of times there exists a subsequence…
Investigates metric degeneracies on symplectic leaves using a generalized gradient flow.
Toda flow explained as a porous medium equation.
In the context of generalized geometry we first show how the Courant bracket helps to define connections with skew torsion and then investigate a five-dimensional invariant functional and its associated geometry. A Hamiltonian flow arising from this corresponds to a version of the Nahm equations using the Courant brack…
Study of Laplacian flow and solitons for G2-structures on homogeneous spaces.
We study curvature flows in the locally homogeneous case (e.g. compact quotients of Lie groups, solvmanifolds, nilmanifolds) in a unified way, by considering a generic flow under just a few natural conditions on the broad class of almost-hermitian structures. As a main tool, we use an ODE system defined on the variety …
Study how large-scale flows align small-scale vortices in 3D Euler equations.
We study the evolution of homogeneous Ricci solitons under the bracket flow, a dynamical system on the space of all homogeneous spaces of dimension n with a q-dimensional isotropy, which is equivalent to the Ricci flow for homogeneous manifolds. We prove that algebraic solitons (i.e. the Ricci operator is a multiple of…
The main purpose of this note is to prove that any basis of a nilpotent Lie algebra for which all diagonal left-invariant metrics have diagonal Ricci tensor necessarily produce quite a simple set of structural constants; namely, the bracket of any pair of elements of the basis must be a multiple of some of them and onl…
The two-loop renormalization group flow is studied via the induced bracket flow on 3D unimodular Lie groups. A number of steady solitons are found. Some of these steady solitons come from maximally symmetric metrics that are steady, shrinking, or expanding solitons under Ricci flow, while others are not obviously relat…
Kontsevich flow simplified for 2D Poisson structures.
Derives equations for interacting Lie-Poisson systems using 2-cocycle extensions.
We study evolution of (strong Kähler with torsion) SKT structures via the pluriclosed flow on complex nilmanifolds, i.e. on compact quotients of simply connected nilpotent Lie groups by discrete subgroups endowed with an invariant complex structure. Adapting to our case the techniques introduced by Jorge Lauret for stu…
Study infinite dimensional Lie algebras and their Poisson structures from Lie group actions.
New maximal families of compatible Poisson structures derived from geodesically equivalent metrics.
Study left-invariant pseudo-Riemannian metrics on Lie groups focusing on null cone Lie algebras.
Flows on (or variations of) discrete curves in give rise to flows on a subalgebra of functions on that curve. For a special choice of flows and a certain subalgebra this is described by the Toda lattice hierachy. In the paper it is shown that the canonical symplectic structure on , which can be interpre…
We present a new formulation of some basic differential geometric notions on a smooth manifold M, in the setting of nonstandard analysis. In place of classical vector fields, for which one needs to construct the tangent bundle of M, we define a prevector field, which is an internal map from *M to itself, implementing t…
We study the existence of left invariant closed -structures defining a Ricci soliton metric on simply connected nonabelian nilpotent Lie groups. For each one of these -structures, we show long time existence and uniqueness of solution for the Laplacian flow on the noncompact manifold. Moreover, considering th…
The symmetric product of vector fields on a manifold arises when one studies the controllability of certain classes of mechanical control systems. A geometric description of the symmetric product is provided using parallel transport, along the lines of the flow interpretation of the Lie bracket. This geometric interpre…
We develop a general approach to study geometric flows on homogeneous spaces. Our main tool will be a dynamical system defined on the variety of Lie algebras called the bracket flow, which coincides with the original geometric flow after a natural change of variables. The advantage of using this method relies on the fa…
Develops a new framework for generalized Ricci flow on Lie groups.
We prove that the Ricci flow g(t) starting at any metric on the euclidean space that is invariant by a transitive nilpotent Lie group N, can be obtained by solving an ODE for a curve of nilpotent Lie brackets. By using that this ODE is the negative gradient flow of a homogeneous polynomial, we obtain that g(t) is type-…
Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. Generically, the singular set is an embedded one dimensional manifold and there are three type of point…
New bracket unifies nonholonomic dynamics and Hamilton-Jacobi theory.
New bracket theory connects three nonholonomic dynamics models.
This note proves equivalence between Dorfman brackets and lifts, showing universality of the Courant-Dorfman bracket.
Flat connections derived from Poisson brackets on loop spaces.
In this paper, we investigate the geometry of a general class of gradient flows with multiple local maxima. we decompose the underlying space into disjoint regions of attraction and establish the adjacency criterion. The criterion states a necessary and sufficient condition for two regions of attraction of stable equil…
It is shown that two definitions for an exterior differential in superspace, giving the same exterior calculus, yet lead to different results when applied to the Poisson bracket. A prescription for the transition with the help of these exterior differentials from the given Poisson bracket of definite Grassmann parity t…
The paper constructs compatible Poisson brackets on gl(N).
We survey the many instances of derived bracket construction in differential geometry, Lie algebroid and Courant algebroid theories, and their properties. We recall and compare the constructions of Buttin and Vinogradov, and we prove that the Vinogradov bracket is the skew-symmetrization of a derived bracket. Odd (resp…
Researchers attempt to categorify biquandle brackets using Khovanov homology methods.
Extends Nambu-Poisson bracket to superspace R^{n|m}.
Graph complex acts on Poisson bi-vectors, producing universal cocycles.
Explains biquandle brackets and quivers for a topology talk.
New method calculates knot and link biquandle brackets using trace diagrams.
A new framework describes dissipation using a metriplectic 4-bracket.
New biquandle bracket invariants are linked to biquandle 2-cocycles.
New geometric definition of Lie bracket for undirected curves.
New examples show non-trivial parity-biquandle bracket.
Complete integrability proved for SR geodesic flow on S^7.
Abstract: Poisson bracket on shear coordinates relates to Fenchel-Nielsen bracket on gluing parameters.
Kishino's knot is not detected by the fundamental group or the bracket polynomial; these invariants cannot differentiate between Kishino's knot and the unknot. However, we can show that Kishino's knot is not equivalent to unknot by applying either the 3-strand bracket polynomial or the surface bracket polynomial. In th…
Enhances quantum invariants using tribracket brackets.