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.
Improved lattice field theory simulations with local-Autoregressive Conditional Normalizing Flow.
The paper proposes a method to sample quantum field configurations using neural operators and flows.
Finite presentations for skein algebras linked to gauge field theory.
Stochastic normalizing flows improve lattice field theory simulations.
Equivariant neural networks improve performance and generalization in lattice field theory tasks.
For a smooth manifold , possibly with boundary and corners, and a Lie group , we consider a suitable description of gauge fields in terms of parallel transport, as groupoid homomorphisms from a certain path groupoid in to . Using a cotriangulation of , and collections of finite-dimensional…
GPU-accelerated particle methods outperform neural samplers in LFT benchmarks.
Mednykh proved that for any finite group G and any orientable surface S, there is a formula for #Hom(pi_1(S), G) in terms of the Euler characteristic of S and the dimensions of the irreducible representations of G. A similar formula in the nonorientable case was proved by Frobenius and Schur. Both of these proofs use c…
The modular vector field plays an important role in the theory of Poisson manifolds and is intimately connected with the Poisson cohomology of the space. In this paper we investigate its significance in the theory of integrable systems. We illustrate in detail the case of the Toda lattice both in Flaschka and natural c…
See q-alg/9710003 for the corrected version of this paper.
Classifies extended Abelian Chern-Simons theories using quadratic modules.
We formulate the unitary rational orbifold conformal field theories in the algebraic quantum field theory framework. Under general conditions, we show that the orbifold of a given unitary rational conformal field theories generates a unitary modular category. Many new unitary modular categories are obtained. We also sh…
The aim of this short lecture series is to expose the students to the beautiful theory of lattices by, on one hand, demonstrating various basic ideas that appear in this theory and, on the other hand, formulating some of the celebrated results which, in particular, shows some connections to other fields of mathematics.…
Equivariant neural networks improve performance and generalization in complex scalar field theory tasks.
Translationally equivariant neural networks improve performance and generalization in physics problems.
We analyze quantum Yang-Mills theory on using a novel discretization method based on an algebraic analogue of stochastic calculus. Such an analogue involves working with "Gaussian" free fields whose covariance matrix is indefinite rather than positive definite. Specifically, we work with Lie-algebra valu…
We prove that the Kauffman bracket skein algebra of a cylinder over a surface with boundary, defined over complex numbers, is isomorphic to the observables of an appropriate lattice gauge field theory.
We study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical transformations of a remarkable ``ultra-local'' Poisson bracket algebra defined on di…
Deep learning enhances Hamiltonian Monte Carlo for sampling gauge field configurations.
A new discretisation of a doubled, i.e. BF, version of the pure abelian Chern-Simons theory is presented. It reproduces the continuum expressions for the topological quantities of interest in the theory, namely the partition function and correlation function of Wilson loops. Similarities with free spinor field theory a…
A number of recent papers have provided evidence that practical design questions about neural networks may be tackled theoretically by studying the behavior of random networks. However, until now the tools available for analyzing random neural networks have been relatively ad-hoc. In this work, we show that the distrib…
We consider the problem of existence of representations of topological groupoids on a principal bundle and the classification of such representations up to gauge transformation. Such representations naturally occur in various contexts such as gauge theory, lattice gauge fields, equivariant bundles, etc. In the course o…
Researchers classify lattices in a specific four-dimensional group.
We complete the quasi-isometric classification of irreducible lattices in semisimple Lie groups over nondiscrete locally compact fields of characteristic zero by showing that any quasi-isometry of a rank one S-arithmetic lattice in a semisimple Lie group over nondiscrete locally compact fields of characteristic zero is…
Proves a lattice version of the Atiyah-Singer index theorem.
We study prismatics sets analogously to simplical sets except that realization involves prisms, i.e., products of simplices rather than just simplices. Particular examples are the prismatic subdivision of a simplicial set S and the prismatic star of S. Both have the same homotopy type as S and in particular the latter …
New method uses neural maps to efficiently sample lattice QCD distributions.
We study upper bounds for the torsion in homology of nonuniform arithmetic lattices. Together with recent results of Calegari-Venkatesh, this can be used to obtain upper bounds on K2 of the ring of integers of totally imaginary fields.
Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some of the methods of lattice simulations of path integrals for the pricing of optio…
We give a quantum field theoretic derivation of the formula obeyed by the Ray-Singer torsion on product manifolds. Such a derivation has proved elusive up to now. We use a BRST formalism which introduces the idea of an infinite dimensional Universal Gauge Fermion, and is of independent interest being applicable to situ…
We show that the Hilbert space formed from a block spin renormalization construction of a cyclic quantum spin chain (based on the Temperley-Lieb algebra) does not support a chiral conformal field theory whose Hamiltonian generates translation on the circle as a continuous limit of the rotations on the lattice.
We give a brief introduction to the Gauge Theory of Arbitrage. Treating a calculation of Net Present Values (NPV) and currencies exchanges as a parallel transport in some fibre bundle, we give geometrical interpretation of the interest rate, exchange rates and prices of securities as a proper connection components. Thi…
L-CNNs maintain gauge symmetry on non-Abelian lattice theories.
Mathematical proof of index equality for lattice Dirac operators and continuum operators.
New simulation method tackles sign problem in quantum fields.
The standard Feynman diagrammatic approach to quantum field theories assumes that perturbation theory approximates the full quantum theory at small coupling even when a mathematically rigorous construction of the latter is absent. On the other hand, two-dimensional Yang-Mills theory is a rare (if not the only) example …
We show that the quantum field theoretical formulation of the -function theory has a geometrical interpretation within the classical transformation theory of conjugate nets. In particular, we prove that i) the partial charge transformations preserving the neutral sector are Laplace transformations, ii) the basic ver…
L-CNNs preserve gauge symmetry in lattice simulations.
Lattice formulation captures Atiyah-Patodi-Singer index.
We outline the theory of sets with distributive operations: multishelves and multispindles, with examples provided by semi-lattices, lattices and skew lattices. For every such a structure we define multi-term distributive homology and show some of its properties. The main result is a complete formula for the homology o…
Using instanton Floer theory, extending methods due to Froyshov, we determine the definite lattices that arise from smooth 4-manifolds bounded by certain homology 3-spheres. For example, we show that for +1 surgery on the (2,5) torus knot, the only non-diagonal lattices that can occur are E8 and the indecomposable unim…
Unified framework for complex financial networks using lattice theory.
New mathematical proposal for TQFTs using TMF-modules.
The asymptotic lattices and their transformations are studied within the line geometry approach. It is shown that the discrete asymptotic nets are represented by isotropic congruences in the Plucker quadric. On the basis of the Lelieuvre-type representation of asymptotic lattices and of the discrete analog of the Mouta…
Discrete knot theory models use lattice-filtered graphs to detect merging knot components.
L-CNNs approximate gauge actions, revealing fixed points with no lattice artifacts.
My main results are simple formulas for the surface area of d-dimensional lattice polytopes using Ehrhart theory.
This survey is a brief introduction to the theory of hyperbolic buildings and their lattices, with a focus on recent results.