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.
Introduces a new geometric framework for non-perturbative BV-theory.
This paper develops a geometric framework for Wilson surfaces in higher gauge theory.
Perturbative string amplitudes are correctly derived from the string geometry theory, which is one of the candidates of a non-perturbative formulation of string theory. In order to derive non-perturbative effects rather easily, we formulate topological string geometry theory. We derive the perturbative partition functi…
We formalize geometrically the idea that the (de Donder) Hamiltonian formulation of a higher derivative Lagrangian field theory can be constructed understanding the latter as a first derivative theory subjected to constraints.
Develops derived differential geometry for supermanifolds.
We characterize the Lie derivative of spinor fields from a variational point of view by resorting to the theory of the Lie derivative of sections of gauge-natural bundles. Noether identities from the gauge-natural invariance of the first variational derivative of the Einstein(--Cartan)--Dirac Lagrangian provide restric…
Derives localization formulas in Batalin-Vilkovisky formalism.
New theory proves representability of PDE solutions without complex machinery.
Develops derived differential geometry theory.
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…
Propose a model-independent axiomatic framework for derived skein theory.
In this short note we prove that the Farrell-Jones Fibered Isomorphism Conjecture in L-theory, after inverting 2, is true for a group whose some derived subgroup is free.
We discuss Ghys' theorem on 4 zeroes of the Schwarzian derivative and its relation with flattening points of Legendrian curves and Sturm theory.
Paper derives formulas for surface variations in shell theory.
Extends curve theory to non-smooth data with finite curvature and torsion.
Theory for deep neural network approximation of score function and its derivatives.
Derives path-integrals for superstrings on curved backgrounds using string geometry theory.
This paper proves equivalence between derived manifolds and differential graded manifolds.
Introduces Lie-Nijenhuis bialgebroids for Poisson-Nijenhuis groupoids.
Derived differential manifolds are constructed using the usual homotopy theory of simplicial rings of smooth functions. They are proved to be equivalent to derived differential manifolds of finite type, constructed using homotopy sheaves of homotopy rings (D.Spivak), thus preserving the classical cobordism ring. This r…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of multivector and multiform fields is presented using algebraic and analytical tools developed in previous papers.
Study virtual fundamental classes of derived manifolds, proving invariant vanishes.
We investigate LIBOR-based derivatives using a parsimonious field theory interest rate model capable of instilling imperfect correlation between different maturities. Delta and Gamma hedge parameters are derived for LIBOR Caps against fluctuations in underlying forward rates. An empirical illustration of our methodolog…
We develop further the approach to derived differential geometry introduced in Costello's work on the Witten genus. In particular, we introduce several new examples of L-infinity spaces, discuss vector bundles and shifted symplectic structures on L-infinity spaces, and examine in some detail the example of derived loop…
Derives path integrals for perturbative strings on various backgrounds.
I briefly review my proposal about how to extend the geometric Hamilton-Jacobi theory to higher derivative field theories on fiber bundles.
This is the first in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we study theories of supercommutative algebras for which infinitely differentiable functions can be evaluated on elements. Such…
We explain the main concepts of Prospect Theory and Cumulative Prospect Theory within the framework of rational dynamic asset pricing theory. We derive option pricing formulas when asset returns are altered with a generalized Prospect Theory value function or a modified Prelec weighting probability function and introdu…
The p-adic theory of the stock market is presented. It is shown that the price dynamics is very naturally described by the adelic function. The procedure of derivation of the functional integral formulation of adelic type is derived from microscopic models using generalized supercoherent states.
Study gauged supergravity, M5-branes, and class R theories, constraining supergravity coefficients and calculating partition functions.
Some problems with the recent stimulating proposal of a ``Gauge Theory of Finance'' by Ilinski and collaborators are outlined. First, the derivation of the log-normal distribution is shown equivalent both in information and mathematical content to the simpler and well-known derivation, dating back from Bachelier and Sa…
Enhances conformal geometry in higher dimensions with infinite-dimensional algebra.
A new method analyzes topological B-model on a torus using doubled geometry.
A quantum field theory for Spin(7)-instantons derived from moduli spaces.
We derive a discrete analogue of Morse-Bott theory on CW complexes and use this discrete Morse-Bott function to do some Conley theory analysis. It turns out that our discrete Morse-Bott theory is indeed a generalization of Forman's discrete Morse theory.
Continues work on derived manifolds and symplectic schemes, constructing virtual classes.
We combine general equilibrium theory and theorie generale of stochastic processes to derive structural results about equilibrium state prices.
Revises mean-field theory of Santa Fe model using kinetic theory.
New framework for higher-order singular-value derivatives of rectangular matrices.
We show how the theory of invariant principal bundle connections for reductive homogeneous spaces can be applied to determine the holonomy of generalised Killing spinor covariant derivatives of the form in a purely algebraic and algorithmic way, where is a left-invariant homo…
New derivation shows how a three-factor learning rule is derived from Oja's rule.
New theory of distributions on spaces with singular submanifolds.
Free differential algebras (FDA's) provide an algebraic setting for field theories with antisymmetric tensors. The "presentation" of FDA's generalizes the Cartan-Maurer equations of ordinary Lie algebras, by incorporating p-form potentials. An extended Lie derivative along antisymmetric tensor fields can be defined, an…
It is a classic result that the geometry of the total space of a principal bundle with reference to the action of the bundle's structure group is codified in the bundle's operation, a collection of derivations comprising the de Rham differential and the contraction and Lie derivatives of all vertical vector fields and …
We derive general Novikov-Morse type inequalities in a Conley type framework for flows carrying cocycles, therefore generalizing our results in [FJ2] derived for integral cocycle. The condition of carrying a cocycle expresses the nontriviality of integrals of that cocycle on flow lines. Gradient-like flows are distingu…
The geometry of the total space of a principal bundle with regard to the action of the bundle's structure group is elegantly described by the bundle's operation, a collection of derivations consisting of the de Rham differential and the contraction and Lie derivatives of all vertical vector fields and satisfying the si…
Unified framework connects deformation theory and derived categories for multiparameter persistence.
Derives adjoint polynomials of torus knots in explicit form.