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.
Study uses geometric algebra to analyze credit cycles, revealing dangerous feedback loops.
New algebraic framework for Jacobi manifolds connects geometric mechanics and dimensional analysis.
Study non-integer power-law potentials for Schrödinger operators using Lie-Rinehart algebras.
New proof found for Khovanov's assertion about Frobenius algebra twists.
Hilbert(ian) A-modules over finite von Neumann algebras A with a faithful normal trace state (from global analysis) and Hilbert W*-modules over A (from operator algebra theory) are compared, and a categorical equivalence is established. The correspondence between these two structures sheds new light on basic results in…
Geometric AD framework simplifies derivative computation in JAX.
The paper proposes a method to compute higher infinitesimals in numerical and symbolic analysis.
Efficiently solves inverse PDE problems with Gaussian processes.
We classify the algebraic curvature tensors which are both Osserman and complex Osserman in all but a finite number of exceptional dimensions.Information concerning the possible eigenvalue structures, which is provided by methods of algebraic topology, plays a central role in the analysis.
Isomorphic algebra connects Toeplitz to Heisenberg group.
Unified framework for complex, split-complex, and dual numbers.
This paper offers a new algebraic perspective of GCCA using subspace intersection.
Novel analysis of neural networks using geometric algebra and convex optimization.
It is shown that the non-trivial cocycles on simple Lie algebras may be used to introduce antisymmetric multibrackets which lead to higher-order Lie algebras, the definition of which is given. Their generalised Jacobi identities turn out to be satisfied by the antisymmetric tensors (or higher-order `structure constants…
Develops method to construct Lie algebra weight system kernel using Vogel algebra.
The problem of determining the volume of a tubular neighbourhood has a long and rich history. Bounds on the volume of neighbourhoods of algebraic sets have turned out to play an important role in the probabilistic analysis of condition numbers in numerical analysis. We present a self-contained derivation of bounds on t…
The paper analyzes privacy leakage in federated learning using linear algebra and optimization theory.
We give a global picture of the Ricci flow on the space of three-dimensional, unimodular, nonabelian metric Lie algebras considered up to isometry and scaling. The Ricci flow is viewed as a two-dimensional dynamical system for the evolution of structure constants of the metric Lie algebra with respect to an evolving or…
Study local and global aspects of complex plane curve embeddings.
Survey on symmetry in manifold structures.
Geometric analysis on real analytic manifolds using seminorms.
Smooth algebra analysis for one-dimensional singular foliations.
Witt algebra acts on Khovanov-Rozansky homology of links.
We discuss and develop some connections between analysis on singular spaces and operator algebras, as presented in my sequence of four lectures at the conference "Noncommutative geometry and applications," Frascati, Italy, June 16-21, 2014. Therefore this paper is mostly a survey paper, but the presentation is new, and…
Researchers solve a 25-year-old conjecture about vector fields.
Some natural hidden symmetries in the Verma modules over the Virasoro algebra are constructed in terms of geometric quantization. Their differential geometric meaning is established and their expression via -conformal symmetries in the Verma modules over the Lie algebra is found. The analysis and the unr…
The paper explores geometric and algebraic structures on Lie groups.
A question of Griffiths-Schmid asks when the monodromy group of an algebraic family of complex varieties is arithmetic. We resolve this in the affirmative for the class of algebraic surfaces known as Atiyah-Kodaira manifolds, which have base and fibers equal to complete algebraic curves. Our methods are topological in …
Study differential and integral calculus on noncommutative C*-algebras.
We develop an algebraic framework for the description and analysis of financial behaviours, that is, behaviours that consist of transferring certain amounts of money at planned times. To a large extent, analysis of financial products amounts to analysis of such behaviours. We formalize the cumulative interest compliant…
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…
Machine learning accelerates Lie algebra computations.
We solved the Schr{ö}dinger equation for a particle in a uniform magnetic field in the n-dimensional torus. We obtained a complete set of solutions for a broad class of problems; the torus T^n = R^n / Λ is defined as a quotient of the Euclidean space R^n by an arbitrary n-dimensional lattice Λ. The lattice is not neces…
New transforms improve signal classification and data analysis.
We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm 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 of the plane. Compared to …
We explore the graded and filtered formality properties of finitely generated groups by studying the various Lie algebras over a field of characteristic 0 attached to such groups, including the Malcev Lie algebra, the associated graded Lie algebra, the holonomy Lie algebra, and the Chen Lie algebra. We explain how thes…
Study of skein invariants on tori for various groups and quantum parameters.
This work speeds up fHMM analysis by tensor algebra.
When solving data analysis problems it is important to integrate prior knowledge and/or structural invariances. This paper contributes by a novel framework for incorporating algebraic invariance structure into kernels. In particular, we show that algebraic properties such as sign symmetries in data, phase independence,…
Lecture notes on BGG complexes using Lie groups and algebras.
Into a geometric setting, we import the physical interpretation of index theorems via semi-classical analysis in topological quantum field theory. We develop a direct relationship between Fedosov's deformation quantization of a symplectic manifold X and the BV quantization of a one-dimensional sigma model with target X…
Stable algebraic filters improve neural network performance.
Generalized diffusion type equations are considered and point symmetry analysis is applied to them. The equations with extremal order point symmetry algebras are described. Some old geometrical results are rederived in connection with theory of these equation.
We prove that the set of non-degenerate second order maximally superintegrable systems in the complex Euclidean plane carries a natural structure of a projective variety, equipped with a linear isometry group action. This is done by deriving the corresponding system of homogeneous algebraic equations. We then solve the…
The paper proves estimates for Hodge Laplacians on Lie groups.
The amoebas associated to algebraic varieties are certain concave regions in the Euclidean space whose shape reminds biological amoebas. This term was formally introduced to Mathematics in 1994 by Gelfand, Kapranov and Zelevinski. Some traces of amoebas were appearing from time to time, even before the formal introduct…
Defines tensor eigenvalues and singular values without basis, simplifying analysis.
Flat Hermitian Lie algebras are always Kähler.