arXiv research

Veech groups uniformize Teichmüller geodesic curves in Riemann moduli space. Recently, examples of infinitely generated Veech groups have been given. We show that these can even have infinitely many cusps and infinitely many infinite ends. We further show that examples exist for which each direction of an infinite end …

This paper is one step toward infinite energy gauge theory and the geometry of infinite dimensional moduli spaces. We generalize a gluing construction in the usual Yang-Mills gauge theory to an ``infinite energy'' situation. We show that we can glue an infinite number of instantons, and that the resulting instantons ha…

Derives PF-ODE for infinite-dimensional functions, improving function generation tasks.

In this preliminary work, we study the generalization properties of infinite ensembles of infinitely-wide neural networks. Amazingly, this model family admits tractable calculations for many information-theoretic quantities. We report analytical and empirical investigations in the search for signals that correlate with…

We construct a infinite-dimensional manifold structure adapted to analytic Lie pseudogroups of infinite type. More precisely, we prove that any isotropy subgroup of an analytic Lie pseudogroup of infinite type is a regular infinite-dimensional Lie group, modelled on a locally convex strict inductive limit of Banach spa…

Study shows quotient group is infinitely generated.

Study infinite genus surfaces and Schottky groups for uniformization.

In this paper, for a non compact and orientable surface $S$ been either: the Infinite Loch Ness monster, the Cantor tree and the Blooming Cantor tree, we construct explicitly an infinitely generated Fuchsian group $Γ<PSL(2,\mathbb{R})$, such that the quotient $\mathbb{H}/Γ$ is a hyperbolic surface homeomorphic to $S$.

Generates special homeomorphisms for complex surfaces.

We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense. We show that the graphs we construct are generally connected, infinite diameter a…

The paper provides infinite presentations for surface groups.

Study generates infinite circle packings with a specific property.

We extend rectified flow to infinite-dimensional Hilbert space.

Big mapping class groups of infinite type surfaces have infinite asymptotic dimension.

Involutions generate mapping class groups of infinite surfaces.

Study of CB generating sets for infinite-type surfaces.

VC dimensions of group CNNs are infinite for certain kernels and groups.

The paper extends Cartan development to infinite dimensional Lie groups.

Infinite-dimensional SBDMs improve image generation across multiple resolutions.

The paper explores non-amenability in infinite-type surfaces and graphs.

Infinite-dimensional diffusion models tackle generative tasks for complex data.

Study infinite group presentations and their Dehn functions.

The twisting technique creates infinite links.

Paper introduces infinite-dimensional generative models using Doob's h-transform.

Study of pure mapping class groups on infinite graphs.

Multitwists cannot generate all compactly supported mapping class groups on infinite-type surfaces.

We generalize Bonahon's characterization of geometrically infinite torsion-free discrete subgroups of PSL(2, $\mathbb{C}$) to geometrically infinite discrete isometry subgroups in the case of rank 1 symmetric spaces, and, under the assumption of bounded torsion, to the case of negatively pinched Hadamard manifolds. Eve…

In this paper we study the rigidity of infinite volume 3-manifolds with sectional curvature $-b^2\le K\le -1$ and finitely generated fundamental group. In-particular, we generalize the Sullivan's quasi-conformal rigidity for finitely generated fundamental group with empty dissipative set to negative variable curvature …

Improves deep generative models to generate images of any size.

We show that the limiting Khovanov chain complex of any infinite positive braid categorifies the Jones-Wenzl projector. This result extends Lev Rozansky's categorification of the Jones-Wenzl projectors using the limiting complex of infinite torus braids. We also show a similar result for the limiting Lipshitz-Sarkar-Kh…

Extends cohomology theory for infinite volume transformation groups.

Study of endperiodic maps on infinite graphs, proving homotopy and eigenvalue properties.

Knots generating infinite subgroup bound rational homology balls.

Suppose that $X,X'$ are simply-connected closed exotic 4-manifolds. It is well-known that $X'$ is obtained by an order 2 cork twist of $X$. We give an infinite exotic family of 4-manifolds not generated by any infinite order cork. This is the first example admitting such a condition. We prove a necessary condition of 4…

Alexander's conjecture extended to infinite simplicial complexes.

This paper reviews recent advances in Bayesian nonparametric techniques for constructing and performing inference in infinite hidden Markov models. We focus on variants of Bayesian nonparametric hidden Markov models that enhance a posteriori state-persistence in particular. This paper also introduces a new Bayesian non…

Study shows symplectic mapping groups of K3 surfaces are infinitely generated.

In this paper, we generalize Bonahon's characterization of geometrically infinite torsion-free discrete subgroups of PSL(2, $\mathbb{C}$) to geometrically infinite discrete subgroups $Γ$ of isometries of negatively pinched Hadamard manifolds $X$. We then generalize a theorem of Bishop to prove that every discrete geome…

This paper presents a natural extension of stagewise ranking to the the case of infinitely many items. We introduce the infinite generalized Mallows model (IGM), describe its properties and give procedures to estimate it from data. For estimation of multimodal distributions we introduce the Exponential-Blurring-Mean-Sh…

Develops infinite-dimensional Kempf-Ness theory for complexification-free groups.

Smooth structures on infinite dimensional Grassmannians and non-commutative cross-ratios.

Deep neural networks' infinite-width behavior approximated by Gaussian models.

Accessible groups with infinitely many ends have infinitely many twisted conjugacy classes.

It is known that finitely generated FI-modules over a field of characteristic 0 are Noetherian. We generalize this result to the abstract setting of an infinite EI category satisfying certain combinatorial conditions.

We prove that rational homology of the Torelli group of genus g is infinite dimensional, provided g>6. This means that rational homology of the Torelli space of genus g>6 is infinite dimensional. The Torelli groups with marked points are also considered. In addition, we prove that rational homology of the subgroup of t…

Study geodesics on graphs with random lengths, proving bi-infinite paths exist.

The paper solves curvature problems on infinite hyperbolic surfaces.

The paper constructs manifolds with infinite holes from a given manifold.