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 formal vertex laws related to Lie conformal algebras.
Global group laws connect equivariant bordism rings to formal group laws.
Generalizes Quillen's theorem to equivariant settings.
In this paper we will present Lagrangian and Hamiltonian -symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using symmetries and pseudosymmetries, without the help of a Noether type theorem, we will o…
This is an extended write-up of a talk given in April, 1993 in honor of Raoul Bott's 70th birthday. We first illustrate how some traditional topological and geometric invariants obey ``gluing laws'' inspired by those in classical and quantum field theory. Here we discuss characteristic numbers, particularly the Euler n…
In this paper we study symmetries, Newtonoid vector fields, conservation laws, Noether's Theorem and its converse, in the framework of the -symplectic formalism, using the Frölicher-Nijenhuis formalism on the space of -velocities of the configuration manifold. For the case , it is well known that Cartan sy…
The differential system for minimal Lagrangian surfaces in a -dimensional, non-flat, complex space form is an elliptic system defined on the bundle of oriented Lagrangian planes. This is a 6-symmetric space associated with the Lie group SL(3,), and the minimal Lagrangian surfaces arise as th…
The paper investigates Goodhart's law and its impact on goal alignment.
Using properties of the determinant line bundle for a family of elliptic boundary value problems, we explain how the Fock space functor defines an axiomatic quantum field theory which formally models the Fermionic path integral. The 'sewing axiom' of the theory arises as an algebraic pasting law for the determinant of …
Our purpose is to relate the Fokker-Planck formalism proposed by [Friedrich et al., Phys. Rev. Lett. 84, 5224 (2000)] for the distribution of stock market returns to the empirically well-established power law distribution with an exponent in the range 3-5. We show how to use Friedrich et al.'s formalism to predict that…
This work explains scaling laws as redundancy laws in deep learning.
This paper provides a description of an algebraic setting for the Lagrangian formalism over graded algebras and is intended as the necessary first step towards the noncommutative C-spectral sequence (variational bicomplex). A noncommutative version of integration procedure, the notion of adjoint operator, Green's formu…
Novel groups exhibit contradictory behaviors with respect to Burnside laws.
We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl's law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the D…
Paper formalizes anti-discrimination law in automated systems.
Surveying fairness formalizations in machine learning for prediction.
Noether's First Theorem yields conservation laws for Lagrangians with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation laws. In recent work the authors showed the mathematical structure behind both th…
Unified physics field theories through a general conservation law.
Improved estimate for remainder term in Weyl law for congruence subgroups of Chevalley groups.
We formulate the theory of nearly autoparallel maps (generalizing conformal transforms) of locally anisotropic spaces and define the nearly autoparallel integration as the inverse operation to both covariant derivation and deformation of connections by nearly autoparallel maps. By using this geometric formalism we cons…
Algorithm designs neural group actions for symmetric transformations.
Paper examines the structure of stochastic gradients in deep learning.
We study the general structure of formal perturbative solutions to the Hamiltonian perturbations of spatially one-dimensional systems of hyperbolic PDEs. Under certain genericity assumptions it is proved that any bihamiltonian perturbation can be eliminated in all orders of the perturbative expansion by a change of coo…
Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous success in describing, among others, the particular stationary state correspondin…
We propose an extension of the differential system for constant mean curvature (CMC) surfaces in a three dimensional space form to an associated hierarchy of evolution equations by the higher-order commuting symmetries. The infinite sequence of higher-order conservation laws of CMC surfaces admit the corresponding exte…
Deviation inequalities and limit laws for random walks on metric spaces.
In this paper we study a class of physical systems that combine a finite number of mechanical and thermodynamic observables. We call them finite dimensional thermo-mechanical systems. We introduce these systems by means of simple examples. The evolution equations of the involved observables are obtained in each example…
Solves Cauchy problem for a KP hierarchy on non-formal operators and relates to diffeomorphisms.
We recall the construction of non-formal deformation quantization of the Poincare Group ISO(1,1) on its coadjoint orbit and exhibit the associated non-formal star-exponentials.
Noether's Theorem yields conservation laws for a Lagrangian with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation laws. The aim of this paper is to explain the mathematical structure of both the Euler…
Survey on finite dimensional Lie groups over real numbers.
The paper explores connections between braids, links, and cobordisms using algebraic methods.
Report on formalizing differential geometry in Lean.
Discover conservation laws from trajectories using a neural network.
The main aim of this paper is the construction of a smooth (sometimes called differential) extension \hat{MU} of the cohomology theory complex cobordism MU, using cycles for \hat{MU}(M) which are essentially proper maps W\to M with a fixed U(n)-structure and U(n)-connection on the (stable) normal bundle of W\to M. Cruc…
The paper defines symmetries in no-arbitrage markets.
We explore homotopies in quantum field theory formalism.
The three-state agent-based 2D model of financial markets as proposed by Giulia Iori has been extended by introducing increasing trust in the correctly predicting agents, a more realistic consultation procedure as well as a formal validation mechanism. This paper shows that such a model correctly reproduces the three f…
Bitcoin price prediction models fail to outperform a simple 'today's price' baseline, especially at longer horizons.
The study shows strong formality in certain complex manifolds.
New research shows transparent treatment disparity is better for achieving impact parity.
Study revisits Bondi mass and discusses memory effect in polyhomogeneous spacetimes.
Unified geometric formulation of Maxwell-Vlasov system using presymplectic and symmetry reduction.
In this note, we address the following question: Which 1-formal groups occur as fundamental groups of both quasi-Kähler manifolds and closed, connected, orientable 3-manifolds. We classify all such groups, at the level of Malcev completions, and compute their coranks. Dropping the assumption on realizability by 3-manif…
Formula for branching coefficients of symmetric pairs.
Proof of boundedness of quasimorphisms for certain Lie groups.
Study non-formal pseudo-differential operators over formal ones.
We announce ultrametric analogues of the results of Kleinbock-Margulis for shrinking target properties of semisimple group actions on symmetric spaces. The main applications are S-arithmetic Diophantine approximation results and logarithm laws for buildings, generalizing the work of Hersonsky-Paulin on trees.