arXiv research

Hybrid subgroups found in non-arithmetic PU(2,1) lattices.

Hybrid lattices produce subgroups of PU(n,1) from PU(n-1,1) lattices.

Researchers reinterpret complex hyperbolic orbifolds using line arrangements.

We show that the number of noncommensurable lattices, hence also that of maximal lattices in SO(1,n) is at least exponential. To do so we construct large families of noncommensurable hybrid hyperbolic (Gromov/Piatetski-Shapiro) manifolds.

New curvature measure on graphs improves diameter and eigenvalue bounds.

New method uses neural maps to efficiently sample lattice QCD distributions.

Simplicial, piecewise-flat discretizations of manifolds provide a clear path towards curvature analysis on discrete geometries and for solutions of PDE's on manifolds of complex topologies. In this manuscript we review and expand on discrete exterior calculus methods using hybrid domains. We then analyze the geometric …

Proves a limit on hyperplanes in complex manifolds.

Hybrid and end-to-end models compare in syllable recognition.

We construct a discrete form of Hamilton's Ricci flow (RF) equations for a d-dimensional piecewise flat simplicial geometry, S. These new algebraic equations are derived using the discrete formulation of Einstein's theory of general relativity known as Regge calculus. A Regge-Ricci flow (RRF) equation is naturally asso…

New algorithm reduces autocorrelation in HMC for lattice field theories.

This paper extends AD techniques to Monte Carlo processes for efficient derivative calculation.

New non-arithmetic lattice found in PU(3,1)

This work improves motion planning for quadcopters by learning and reasoning about controller performance.

New property identifies arithmetic lattices from nonuniform lattices.

We present NN-grams, a novel, hybrid language model integrating n-grams and neural networks (NN) for speech recognition. The model takes as input both word histories as well as n-gram counts. Thus, it combines the memorization capacity and scalability of an n-gram model with the generalization ability of neural network…

New lattice stick knot condition identified.

Simplified proof for lattice link projections.

This work compares lattice-free and lattice-based training criteria for LVCSR.

Research finds bounds for knots in hexagonal lattice and classifies 11-stick knots.

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…

Course on arithmetic lattices at EPFL.

New lattices from 4-manifolds show manifold properties.

Upper bound for lattice stick number of spatial graphs.

New thin subgroups found in special linear groups via bending techniques.

New rigidity theorem for product of lattices.

This paper studies the covolumes of nonuniform arithmetic lattices in PU(n, 1). We determine the smallest covolume nonuniform arithmetic lattices for each n, the number of minimal covolume lattices for each n, and study the growth of the minimal covolume as n varies. In particular, there is a unique lattice (up to conj…

The paper finds incommensurable lattices in complex models of Baumslag-Solitar groups.

Proves a lattice version of the Atiyah-Singer index theorem.

Defines non-parabolic curves in spatial hybrid space with applications.

Vertex distortion measures how far lattice knots deviate from straight lines.

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…

The paper proves residual finiteness of certain lattices and constructs surfaces with specific fundamental groups.

Proves properties of arithmetic lattices and hyperbolic manifolds.

A celebrated theorem of Hadwiger states that the Euler-Poincaré characteristic is the the unique invariant and continuous valuation on the distributive lattice of compact polyhedra in R^n that assigns value one to each convex non-empty such polyhedron. This paper provides an analogue of Hadwiger's result for finitely p…

The cubic lattice stick index of a knot type is the least number of sticks necessary to construct the knot type in the 3-dimensional cubic lattice. We present the cubic lattice stick index of various knots and links, including all (p,p+1)-torus knots, and show how composing and taking satellites can be used to obtain t…

New method finds lattice polygons that can be dissected into triangles with integer areas.

L-CNNs approximate gauge actions, revealing fixed points with no lattice artifacts.

The paper refines transformations of lattice diagrams and introduces dotted diagrams.

Classifies knots by lattice size, finding unknot ratios and crossing numbers.

Let $G$ be a simply connected, solvable Lie group and $Γ$ a lattice in $G$. The deformation space $\mathcal{D}(Γ,G)$ is the orbit space associated to the action of $\Aut(G)$ on the space $\mathcal{X}(Γ,G)$ of all lattice embeddings of $Γ$ into $G$. Our main result generalises the classical rigidity theorems of Mal'tsev…

Proves effective slope gaps for lattice surfaces.

Improved lattice field theory simulations with local-Autoregressive Conditional Normalizing Flow.

Study answers arithmeticity question for normal subgroup of lattices.

Study investigates lattices fibring over the circle, focusing on BNSR invariants.

One type of switch simplifies operations on lattice knots.

New lattices in higher dimensions have dense surface subgroups.

Defines and analyzes the holonomy Lie algebra of geometric lattices.