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.
Spin Lefschetz fibrations can represent any group and lattice point.
The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but non-linear and non-convex constraint. The main results of this paper are significan…
The paper refines transformations of lattice diagrams and introduces dotted diagrams.
The paper examines deformations of simple dotted graphs made of circles.
We address the problem of classifying discrete differential-geometric Poisson brackets (dDGPBs) of any fixed order on target space of dimension 1. It is proved that these Poisson brackets (PBs) are in one-to-one correspondence with the intersection points of certain projective hypersurfaces. In addition, they can be re…
New methods classify convex lattice polygons for affine dimers.
Discrete knot theory models use lattice-filtered graphs to detect merging knot components.
Counting tripods on a flat torus using lattice point counting.
Growth rate of Dehn twist lattice points in Teichmüller space is slower than mapping class group lattice points.
L-CNNs approximate gauge actions, revealing fixed points with no lattice artifacts.
Regular integer lattices are characterized by k unit vectors that build up their generator matrices. These have rank k for D-lattices, and are rank-deficient for A-lattices, for E_6 and E_7. We count lattice points inside hypercubes centered at the origin for all three types, as if classified by maximum infinity norm i…
We show that twin building lattices have linear divergence, which implies that all asymptotic cones are without cut-points.
A Teichmuller lattice is the orbit of a point in Teichmuller space under the action of the mapping class group. We show that the proportion of lattice points in a ball of radius r which are not pseudo-Anosov tends to zero as r tends to infinity. In fact, we show that if R is a subset of the mapping class group, whose e…
In this paper, first and second type admissible Mannheim partner curves are defined in pseudo-Galilean space . Moreover, it is proved that the distance between the reciprocal points of both of first and second type admissible Mannheim curves and the torsions of these curves are constant. Furthermore, the relatio…
Study integrability of quantized six-vertex model on torus.
Research examines correlations of complex logarithms of lattice points, showing level repulsion and Poissonian behavior.
We show how to define and count lattice points in the moduli space $\modm_{g,n}$ of genus g curves with n labeled points. This produces a polynomial with coefficients that include the Euler characteristic of the moduli space, and tautological intersection numbers on the compactified moduli space.
A Riemannian symmetric space is a Riemannian manifold in which it is possible to reflect all geodesics through a point by an isometry of the space. On such spaces, we introduce the notion of a distributional lattice, generalizing the notion of lattice. Distributional lattices exist in any Riemannian symmetric space: th…
Deep convolutional neural networks (CNNs) have shown outstanding performance in the task of semantically segmenting images. However, applying the same methods on 3D data still poses challenges due to the heavy memory requirements and the lack of structured data. Here, we propose LatticeNet, a novel approach for 3D sema…
The paper establishes inequalities for convex curves and applies them to lattice point estimates.
We prove that a potential can be reconstructed from the Dirichlet-to-Neumann map for the Schrodinger operator in a fixed admissible 3-dimensional Riemannian manifold . We also show that an admissible metric in a fixed conformal class can be constructed from the Dirichlet-to-Neumann map for $Δ_…
Stability in homology of moduli spaces of admissible covers.
New MCMC method samples from lattice distributions efficiently.
Let $\A$ be a line arrangement in the complex projective plane $\PP^2$. Denote by its complement and by $\M$ the set of points in $\A$ with multiplicity at least 3. A rank one local system on is admissible if roughly speaking the dimension of the cohomology groups can be compu…
Proves effective slope gaps for lattice surfaces.
Method computes harmonic and conformal maps from point clouds.
Counting lattice points in moduli space of Klein surfaces.
We obtain a growth estimate for the number of lattice points inside any Q-Gorenstein cone. Our proof uses the result of Futaki-Ono-Wang on Sasaki-Einstein metric for the toric Sasakian manifold associated to the cone, a Yau's inequality, and the Kawasaki-Riemann-Roch formula for orbifolds.
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 approach proves K-stability of Fano varieties.
We study the topology of admissible-loop spaces on a step-two Carnot group G. We use a Morse-Bott theory argument to study the structure and the number of geodesics on G connecting the origin with a 'vertical' point (geodesics are critical points of the 'Energy' functional, defined on the loop space). These geodesics t…
The paper is a study of geodesic in two-dimensional pseudo-Riemannian metrics. Firstly, the local properties of geodesics in a neighborhood of generic parabolic points are investigated. The equation of the geodesic flow has singularities at such points that leads to a curious phenomenon: geodesics cannot pass through s…
In a joint work with Saji, the second and the third authors gave an intrinsic formulation of wave fronts and proved a realization theorem of wave fronts in space forms. As an application, we show that the following four objects are essentially same; * conformally flat n-manifolds (n>=3) with admissible singular points …
We express the number of lattice points inside certain simplices via Dedekind-Rademacher sums. As an application, we prove a conjecture of Kronheimer and Mrowka in the special case of Brieskorn spheres (with at most 4 singular fibers). This conjecture relates the Euler characteristic of the Seiberg-Witten-Floer homolog…
We define and count lattice points in the moduli space of stable genus g curves with n labeled points. This extends a construction of the second author for the uncompactified moduli space. The enumeration produces polynomials with top degree coefficients tautological intersection numbers on the compactified moduli spac…
Investigates stochastic networks on disordered lattices, converging to Brownian web in 2D.
Let be an irreducible lattice of $\Q$-rank in a semisimple Lie group of noncompact type. We prove that any action of on a $\CAT(0)$ cubical complex has a global fixed point.
In this article we describe cell decompositions of the moduli space of Riemann surfaces and their relationship to a Hurwitz problem. The cells possess natural linear structures and with respect to this they can be described as rational convex polytopes which come equipped with natural integer points and a volume form. …
New method for geodesics of multivariate normals, derived from a Toda lattice.
We prove that any action of a higher rank lattice on a Gromov-hyperbolic space is elementary. More precisely, it is either elliptic or parabolic. This is a large generalization of the fact that any action of a higher rank lattice on a tree has a fixed point. A consequence is that any quasi-action of a higher rank latti…
In this work we will build a fundamental domain for Deligne-Mostow lattices in PU(2,1) with 2-fold symmetry, which complete the whole list of Deligne-Mostow lattices in dimension 2. These lattices were introduced by Deligne and Mostow using monodromy of hypergeometric functions and have been reinterpreted by Thurston a…
Machine learning finds a compact fixed point action for SU(3) gauge theory.
Combining forecasts of 16 ED causes improves accuracy and stability.
The study connects lattices, Garside structures, and weakly modular graphs.
We are concerned with unbounded sets of whose boundary has constant nonlocal (or fractional) mean curvature, which we call CNMC sets. This is the equation associated to critical points of the fractional perimeter functional under a volume constraint. We construct CNMC sets which are the countable union o…
We introduce a criterion that a given bihamiltonian structure allows a local coordinate system where both brackets have constant coefficients. This criterion is applied to the bihamiltonian open Toda lattice in a generic point, which is shown to be locally isomorphic to a Kronecker odd-dimensional pair of brackets with…
Unified framework for complex financial networks using lattice theory.
CDP reduces point cloud dimensions by preserving detour-induced local non-convexity.