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.
Revives Vogel's diagrammatic technique for universal Lie algebra computations.
Decomposes nonconvex polynomials into convex parts using algebraic methods.
The main purpose of this article is to demonstrate three techniques for proving algebraicity statements about circle packings. We give proofs of three related theorems: (1) that every finite simple planar graph is the contact graph of a circle packing on the Riemann sphere, equivalently in the complex plane, all of who…
Proves algebraicity of maps to hyperbolic varieties using specialization techniques.
New techniques solve Riccati equations on 3D manifolds, finding 4th order metric obstructions.
In this paper we construct a parametrization-free embedding technique for numerically evolving reaction-diffusion PDEs defined on algebraic curves that possess an isolated singularity. In our approach, we first desingularize the curve by appealing to techniques from algebraic geometry. We create a family of smooth curv…
We study `constrained generalized Killing (s)pinors', which characterize supersymmetric flux compactifications of supergravity theories. Using geometric algebra techniques, we give conceptually clear and computationally effective methods for translating supersymmetry conditions into differential and algebraic constrain…
We study nilmanifolds admitting Anosov automorphisms by applying elementary properties of algebraic units in number fields to the associated Anosov Lie algebras. We identify obstructions to the existence of Anosov Lie algebras. The case of 13-dimensional Anosov Lie algebras is worked out as an illustration of the techn…
A cohomology theory of the adjoint of Hopf algebras, via deformations, is presented by means of diagrammatic techniques. Explicit calculations are provided in the cases of group algebras, function algebras on groups, and the bosonization of the super line. As applications, solutions to the YBE are given and quandle coc…
Algebraic multigrid speeds up SVM training for large datasets.
The paper describes handle decompositions and Kirby diagrams for plane algebraic curves.
Paper uses algebraic methods to prove an equivariant Poincaré-Hopf theorem.
New method solves SLV models faster using Lie algebra.
Develops method to construct Lie algebra weight system kernel using Vogel algebra.
We compute the equivariant cohomology Chern character of the index of elliptic operators along the leaves of the foliation of a flat bundle. The proof is based on the study of certain algebras of pseudodifferential operators and uses techniques for analizing noncommutative algebras similar to those developed in Algebra…
Two elliptic Kashiwara-Vergne Lie algebras match.
A simplified proof for satellite knot signatures.
Constructs a homotopy Loday algebra from symplectic 2-manifolds.
Defines and extends flat pseudo-Riemannian F-Lie algebras.
We study constrained generalized Killing spinors over the metric cone and cylinder of a (pseudo-)Riemannian manifold, developing a toolkit which can be used to investigate certain problems arising in supersymmetric flux compactifications of supergravity theories. Using geometric algebra techniques, we give conceptually…
Formula for fixed points on noncompact spaces.
If a Lie algebra structures $\gG$ on a vector space is the sum of a family of mutually compatible Lie algebra structures $\gG_i$, we say that $\gG$ is \emph{simply assembled} from $\gG_s$'s. By repeating this procedure several times one gets a family of Lie algebras \emph{assembled} from $\gG_s$'s. The central result o…
Neural decoders improve performance on large algebraic block codes.
New techniques simplify computing geometric index of links in solid tori.
The paper extends algebraic constructions to -graded manifolds and Lie algebroids.
Given a planar curve singularity, we prove a conjecture of Oblomkov-Shende, relating the geometry of its Hilbert scheme of points to the HOMFLY polynomial of the associated algebraic link. More generally, we prove an extension of this conjecture, due to Diaconescu-Hua-Soibelman, relating stable pair invariants on the c…
These lectures given in Montreal in Summer 1997 are mainly based on, and form a condensed survey of, the book by N. Chriss and V. Ginzburg: `Representation Theory and Complex Geometry', Birkhauser 1997. Various algebras arising naturally in Representation Theory such as the group algebra of a Weyl group, the universal …
We present a novel certified and complete algorithm to compute arrangements of real planar algebraic curves. It provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic curves in terms of a cylindrical algebraic decomposition. From a high-level perspective, the…
This paper is a presentation, where we compute the HOMFLYPT Skein module of singular links in the 3-sphere. This calculation is based on some results previously proved by Rabenda and the author on Markov traces on singular Hecke algebras, as well as on classical techniques that allow to pass from the framework of Marko…
We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that a certain number of generic rank-one or generic linear measurements are suffici…
Overview of dynamics in algebraic correspondences and their connections.
New algebraic characterization of sectional curvature bounds using Weitzenböck formulae.
Paper studies homology and cohomology of Temperley-Lieb algebra TL_n(a).
Constructs mixed Hodge structures on Kähler manifolds.
Characterizes pseudo-Anosov mapping classes using cluster algebra techniques.
In his Inventiones paper, Ziller (Invent. Math: 1-22, 1977) computed the integral homology as a graded abelian group of the free loop space of compact, globally symmetric spaces of rank 1. Chas and Sullivan (String Topology, 1999)showed that the homology of the free loop space of a compact closed orientable manifold ca…
UMAP simplifies data visualization while preserving global structure.
The ``classical BRST construction'' as developed by Batalin-Fradkin-Vilkovisky is a homological construction for the reduction of the Poisson algebra of smooth functions on a Poisson manifold by the ideal of functions which vanish on a constraint locus. This ideal is called first class if …
For a simply connected (non-nilpotent) solvable Lie group with a lattice the de Rham and Dolbeault cohomologies of the solvmanifold are not in general isomorphic to the cohomologies of the Lie algebra of . In this paper we construct, up to a finite group, a new Lie algebra $\tilde{\mathfr…
AI can identify simple groups and match algebraic tables, even with limited training.
The paper classifies vector fields on 5D nilpotent Lie groups.
We establish tools to facilitate the computation and application of the Chekanov-Eliashberg differential graded algebra (DGA), a Legendrian-isotopy invariant of Legendrian knots in standard contact three-space. More specifically, we reformulate the DGA in terms of front projection, and introduce the characteristic alge…
New theory disassembles Lie algebras into dyons and triadons.
This article is written for the Proceedings of the Conference on Current Developments in Mathematics in Harvard University, November 16-17, 2007. It is an exposition of the analytic proof of the finite generation of the canonical ring for a compact complex algebraic manifold of general type. It lists and discusses the …
The paper proves the existence of special 3D shapes smoothly embedded in certain spaces.
Paper proves unique tangent maps for complex maps into algebraic varieties.
New displacement technique vanishes bounded cohomology in all degrees.
Introduces noncommutative geometry for modeling quantum spacetime.