Tootfinder

This https://arxiv.org/abs/2402.00354 has been replaced.
link: https://scholar.google.com/scholar?q=a

Uniform twisted homological stability
We prove a homological stability theorem for families of discrete groups (e.g. mapping class groups, automorphism groups of free groups, braid groups) with coefficients in a sequence of irreducible algebraic representations of arithmetic groups. The novelty is that the stable range is independent of the choice of representation. Combined with earlier work of Bergström--Diaconu--Petersen--Westerland this proves the Conrey--Farmer--Keating--Rubinstein--Snaith predictions for all moments of the f…

This https://arxiv.org/abs/2104.07431 has been replaced.
link: https://scholar.google.com/scholar?q=a

One-ended spanning subforests and treeability of groups
We show that several new classes of groups are measure strongly treeable. In particular, finitely generated groups admitting planar Cayley graphs, elementarily free groups, and the group of isometries of the hyperbolic plane and all its closed subgroups. This provides the first examples of one-ended nonamenable groups which are measure strongly treeable. In higher dimensions, we also prove a dichotomy that the fundamental group of a closed aspherical $3$-manifold is either amenable or has stron…

Microsoft, Google, CrowdStrike, and Palo Alto plan a public glossary of state-sponsored hacking groups to ease confusion over the spread of unofficial aliases (Reuters)
https://www.reuters.com/sustainability/boa…

This https://arxiv.org/abs/2209.12996 has been replaced.
link: https://scholar.google.com/scholar?q=a

Rigidity for von Neumann algebras of graph product groups. I. Structure of automorphisms
In this paper we study various rigidity aspects of the von Neumann algebra $L(Γ)$ where $Γ$ is a graph product group \cite{Gr90} whose underlying graph is a certain cycle of cliques and the vertex groups are the wreath-like product property (T) groups introduced recently in \cite{CIOS21}. Using an approach that combines methods from Popa's deformation/rigidity theory with new techniques pertaining to graph product algebras, we describe all symmetries of these von Neumann algebras and reduced …

This https://arxiv.org/abs/2309.01754 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the success probability of the quantum algorithm for the short DLP
Ekerå and Håstad have introduced a variation of Shor's algorithm for the discrete logarithm problem (DLP). Unlike Shor's original algorithm, Ekerå-Håstad's algorithm solves the short DLP in groups of unknown order. In this work, we prove a lower bound on the probability of Ekerå-Håstad's algorithm recovering the short logarithm $d$ in a single run. By our bound, the success probability can easily be pushed as high as $1 - 10^{-10}$ for any short $d$. A key to achieving such a high success…

This https://arxiv.org/abs/2207.12969 has been replaced.
link: https://scholar.google.com/scholar?q=a

Module Categories of the Generic Virasoro VOA and Quantum Groups
In this paper, we prove the equivalence between two ribbon tensor categories. On the one hand, we consider the category of modules of the Virasoro vertex operator algebra with generic central charge (generic Virasoro VOA) generated by those simple modules lying in the first row of the Kac table. On the other hand, we take the category of finite-dimensional type I modules of the quantum group $\mathcal{U}_q (\mathfrak{sl}_{2})$ with $q$ determined by the central charge. This is a continuation of…

This https://arxiv.org/abs/2402.00549 has been replaced.
link: https://scholar.google.com/scholar?q=a

On ordered groups of regular growth rates
We introduce an elementary class of linearly ordered groups, called growth order groups, encompassing certain groups under composition of formal series (e.g. transseries) as well as certain groups $\mathcal{G}_{\mathcal{M}}$ of infinitely large germs at infinity of unary functions definable in an o-minimal structure $\mathcal{M}$. We study the algebraic structure of growth order groups and give methods for constructing examples. We show that if $\mathcal{M}$ expands the real ordered field and g…

This https://arxiv.org/abs/2208.00676 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Pansiot-type subword complexity theorem for automorphisms of free groups
Inspired by Pansiot's work on substitutions, we prove a similar theorem for automorphisms of a free group F of finite rank: if a right-infinite word X represents an attracting fixed point of an automorphism of F, the subword complexity of X is equivalent to n, n log log n, n log n, or n^2. The proof uses combinatorial arguments analogue to Pansiot's as well as train tracks. We also define the recurrence complexity of X, and we apply it to laminations. In particular, we show that attracting lami…

This https://arxiv.org/abs/2409.20359 has been replaced.
link: https://scholar.google.com/scholar?q=a

Curvature estimates for minimal hypersurfaces in the Heisenberg group
This paper examines minimal hypersurfaces in sub-Riemannian Heisenberg groups. We extend the celebrated Simons formula and Kato inequality to the sub-Riemannian setting, and we apply them to obtain integral curvature estimates for stable hypersurfaces. These results lead to structural conditions that imply a Bernstein-type rigidity theorem for smooth, non-characteristic hypersurfaces in the second Heisenberg group.

This https://arxiv.org/abs/2409.19491 has been replaced.
link: https://scholar.google.com/scholar?q=a

Growth of finitely generated subgroups of the topological full groups of inverse semigroups of bounded type
Given an inverse semigroup $G_0$ of bounded type, we show, along with some other assumptions, that if the set of incompressible elements of $G_0$ is finite, then any finitely generated subgroup $G$ of the topological full group $\mathsf{F}(G_0)$ that is orbit equivalent to $G_0$ has subexponential growth with a bounded power in the exponent.

This https://arxiv.org/abs/2201.12881 has been replaced.
link: https://scholar.google.com/scholar?q=a

Oscillating singular integral operators on graded Lie groups revisited
In this work, we extend the Euclidean theory of oscillating singular integrals due to Fefferman and Stein in \cite{Fefferman1970,FeffermanStein1972} to arbitrary graded Lie groups. Our approach reveals the strong compatibility between the geometric measure theory of a graded Lie group and the Fourier analysis associated with Rockland operators. Our criteria are presented in terms of the oscillating Fefferman condition of the kernel of the operator and its group Fourier transform. One of the nov…

This https://arxiv.org/abs/2212.05366 has been replaced.
link: https://scholar.google.com/scholar?q=a

Specialization of Difference Equations and High Frobenius Powers
We study valued fields equipped with an automorphism $σ$ which is locally infinitely contracting in the sense that $α\llσα$ for all $0<α\inΓ$. We show that various notions of valuation theory, such as Henselian and strictly Henselian hulls, admit meaningful transformal analogues. We prove canonical amalgamation results, and exhibit the way that transformal wild ramification is controlled by torsors over generalized vector groups. Model theoretically, we determine the model companion: it i…

This https://arxiv.org/abs/2011.02575 has been replaced.
link: https://scholar.google.com/scholar?q=a

The group of affine transformations of homogeneous spaces with discrete isotropy
We present a method to compute the group of affine transformations of a homogeneous $G$-space under specific conditions: when the group $G$ and the homogeneous $G$-space admit linear connections so that the natural projection is affine, and with discrete isotropy group. If $G$ admits a bi-invariant linear connection, we establish conditions under which the homogeneous space admits an invariant linear connection. As a consequence, when the isotropy group is discrete, their respective groups of a…

This https://arxiv.org/abs/1503.03852 has been replaced.
link: https://scholar.google.com/scholar?q=a

On groups of diffeomorphisms of the interval with finitely many fixed points
In [13], it is proved that any subgroup of $\mathrm{Diff}_{+}^{ω}(I)$ (the group of orientation preserving analytic diffeomorphisms of the interval) is either metaabelian or does not satisfy a law. A stronger question is asked whether or not the Girth Alternative holds for subgroups of $\mathrm{Diff}_{+}^{ω}(I)$. In this paper, we answer this question affirmatively for even a larger class of groups of orientation preserving diffeomorphisms of the interval where every non-identity element has …

This https://arxiv.org/abs/2410.21527 has been replaced.
link: https://scholar.google.com/scholar?q=a

VISTA-SSM: Varying and Irregular Sampling Time-series Analysis via State Space Models
We introduce VISTA, a clustering approach for multivariate and irregularly sampled time series based on a parametric state space mixture model. VISTA is specifically designed for the unsupervised identification of groups in datasets originating from healthcare and psychology where such sampling issues are commonplace. Our approach adapts linear Gaussian state space models (LGSSMs) to provide a flexible parametric framework for fitting a wide range of time series dynamics. The clustering approac…

This https://arxiv.org/abs/1908.10505 has been replaced.
link: https://scholar.google.com/scholar?q=a

Spectral properties of graphs associated to the Basilica group
We provide the foundation of the spectral analysis of the Laplacian on the orbital Schreier graphs of the Basilica group, the iterated monodromy group of the quadratic polynomial $z^2-1$. This group is an important example in the class of self-similar amenable but not elementary amenable finite automata groups studied by Grigorchuk, Żuk, \v Sunić, Bartholdi, Virág, Nekrashevych, Kaimanovich, Nagnibeda et al. We prove that the spectrum of the Laplacian has infinitely many gaps and that the su…