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.
Proves a lattice version of the Atiyah-Singer index theorem.
The paper proposes a method to sample quantum field configurations using neural operators and flows.
L-CNNs maintain gauge symmetry on non-Abelian lattice theories.
Mathematical proof of index equality for lattice Dirac operators and continuum operators.
L-CNNs preserve gauge symmetry in lattice simulations.
Equivariant neural networks improve performance and generalization in lattice field theory tasks.
Lattice formulation captures Atiyah-Patodi-Singer index.
Stochastic normalizing flows improve lattice field theory simulations.
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.
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.
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.
Research finds bounds for knots in hexagonal lattice and classifies 11-stick knots.
New deformations of lattice cohomology help calculate knot invariants.
Finite presentations for skein algebras linked to gauge field theory.
The B-quadrilateral lattice (BQL) provides geometric interpretation of Miwa's discrete BKP equation within the quadrialteral lattice (QL) theory. After discussing the projective-geometric properties of the lattice we give the algebro-geometric construction of the BQL ephasizing the role of Prym varieties and the corres…
In a way similar to the continuous case formally, we define in different but equivalent manners the difference discrete connection and curvature on discrete vector bundle over the regular lattice as base space. We deal with the difference operators as the discrete counterparts of the derivatives based upon the differen…
In this paper, we examine Kitaev's lattice model for an arbitrary complex, semisimple Hopf algebra. We prove that this model gives the same topological invariants as Turaev-Viro theory. Using the description of Turaev-Viro theory as an extended TQFT, we prove that the excited states of the Kitaev model correspond to Tu…
L-CNNs preserve gauge symmetry in neural networks.
GPU-accelerated particle methods outperform neural samplers in LFT benchmarks.
L-CNNs learn gauge invariant quantities on lattices.
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…
The paper refines transformations of lattice diagrams and introduces dotted diagrams.
We find two bases for the lattices of the SU(2)-TQFT-theory modules of the torus over given rings of integers. We use variant of the bases defined in [GMW]for the lattices of the SO(3)-TQFT-theory modules of the torus. Moreover, we discuss the quantization functors (V_{p},Z_{p}) for p=1, and p=2. Then we give concrete …
New invariant unifies two theories of 3-manifolds, recovering quantum invariants.
We give an overview on the tt*-geometry defined for isolated hypersurface singularities and tame functions via Brieskorn lattices. We discuss nilpotent orbits in this context, as well as classifying spaces of Brieskorn lattices and (limits of) period maps.
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…
Develops a new sampling method for gauge theories.
We find bases for naturally defined lattices over certain rings of integers in the SU(2)-TQFT-theory modules of surfaces. We consider the TQFT where the Kauffman's A variable is a root of unity of order four times an odd prime. As an application, we show that the Frohman Kania-Bartoszynska ideal invariant for 3-manifol…
This paper solves PDEs for embedding discrete lattices into smooth manifolds.
In any connected non-compact semi-simple Lie group without factors locally isomorphic to SL_2(R), there can be only finitely many lattices (up to isomorphism) of a given covolume. We show that there exist arbitrarily large families of pairwise non-isomorphic arithmetic lattices of the same covolume. We construct these …
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.…
Generalizes Kauffman's clock theorem to surfaces.
Classifies extended Abelian Chern-Simons theories using quadratic modules.
This paper introduces lattice representations for efficient discrete learning.
Improved sampling for gauge theory with SNFs.
The study examines knot probabilities in confined lattice polygons.
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…
We explain how, starting with a stack of D4-branes ending on an NS5-brane in type IIA string theory, one can, via T-duality and the topological-holomorphic nature of the relevant worldvolume theories, relate (i) the lattice models realized by Costello's 4d Chern-Simons theory, (ii) links in 3d analytically-continued Ch…
We derive results on the distribution of directions of saddle connections on translation surfaces using only the Birkhoff ergodic theorem applied to the geodesic flow on the moduli space of translation surfaces. Our techniques, together with an approximation argument, also give an alternative proof of a weak version of…
We present an intriguing question about lattice points in triangles where Pick's formula is "almost correct". The question has its origin in knot theory, but its statement is purely combinatorial. After more than 30 years the topological question was recently solved, but the lattice point problem is still open.
New framework for detecting complex interactions in multivariate data.
See q-alg/9710003 for the corrected version of this paper.
We find coordinates, the metric tensor, the inverse metric tensor and the Laplace-Beltrami operator for the orbit space of Hamiltonian SU(2) gauge theory on a finite, rectangular lattice. This is done using a complete axial gauge fixing. The Gribov problem can be completely solved, with no remaining gauge ambiguities.