Tootfinder

The Document Outline Algorithm failed (was poorly spec’d, never implemented). Many other ideas come and gone.
The latest (from 2019), `headinglevelstart`, is about to get prototyped in Chromium:
https://groups.google.com/a/chromium.org/g/blin…

This https://arxiv.org/abs/2401.17893 has been replaced.
link: https://scholar.google.com/scholar?q=a

Cosmological solutions in the Brans-Dicke theory via invariants of symmetry groups
We proceed to obtain an exact analytical solution of the Brans-Dicke (BD) equations for the spatially flat ($k=0$) Friedmann-Lamaitre-Robertson-Walker (FLRW) cosmological model in both cases of the absence and presence of the cosmological constant. The solution method that we use to solve the field equations of the BD equations is called the "invariants of symmetry groups method" (ISG-method). This method is based on the extended Prelle-Singer (PS) method and it employs the Lie point symmetry, …

This https://arxiv.org/abs/2301.01573 has been replaced.
link: https://scholar.google.com/scholar?q=a

Endomorphism Algebras and Automorphism Groups of certain Complex Tori
We study the endomorphism algebra, the automorphism group and the Hodge group of complex tori of complex tori, whose second rational cohomology group enjoys a certain Hodge property introduced by F. Campana.

This https://arxiv.org/abs/1706.03376 has been replaced.
link: https://scholar.google.com/scholar?q=a

Strongly Dependent Ordered Abelian Groups and Henselian Fields
Strongly dependent ordered abelian groups have finite dp-rank. They are precisely those groups with finite spines and $|\{p\text{ prime}:[G:pG]=\infty\}|<\infty$. We apply this to show that if $K$ is a strongly dependent field, then $(K,v)$ is strongly dependent for any henselian valuation $v$.

This https://arxiv.org/abs/2212.02249 has been replaced.
link: https://scholar.google.com/scholar?q=a

The symbol length for elementary type pro-$p$ groups and Massey products
For a prime number $p$ and an integer $m\geq2$, we prove that the symbol length of all elements of $m$-fold Massey products in $H^2(G,\mathbb{F}_p)$, for pro-$p$ groups $G$ of elementary type, is bounded by $(m^2/4)+m$. Assuming the Elementary Type Conjecture, this applies to all finitely generated maximal pro-$p$ Galois groups $G=G_F(p)$ of fields $F$ which contain a root of unity of order $p$. More generally, we provide such a uniform bound for the symbol length of all pullbacks $ρ^*(\barω)…

But hey, remember (especially tech folks) that sponsorship doesn’t affect how an organisation behaves.
https://ar.al/2019/01/11/i-was-wrong-about-google-and-facebook-theres-nothing-wrong-with-them-so-say-we-all/…

I was wrong about Google and Facebook: there’s nothing wrong with them (so say we all)
It’s always difficult admitting you’re wrong. But sometimes, it’s exactly what you have to do in the face of overwhelming evidence to the contrary. So, today, I admit that I was wrong about Google, Facebook, and surveillance capitalism in general being toxic for our human rights and democracy. You see, it simply cannot be true given how they are endorsed by some of the most well-respected groups and organisations in the world.

This https://arxiv.org/abs/2103.06930 has been replaced.
link: https://scholar.google.com/scholar?q=a

Virtual algebraic fibrations of surface-by-surface groups and orbits of the mapping class group
We show that a conjecture of Putman--Wieland, which posits the nonexistence of finite orbits for higher Prym representations of the mapping class group, is equivalent to the existence of surface-by-surface and surface-by-free groups which do not virtually algebraically fiber. While the question about the existence of such groups remains open, we will show that there exist free-by-free and free-by-surface groups which do not algebraically fiber (hence fail to be virtually RFRS).

This https://arxiv.org/abs/2203.11148 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Todd-Coxeter Algorithm for Semigroups and Monoids
In this paper we provide an account of the Todd-Coxeter algorithm for computing congruences on semigroups and monoids. We also give a novel description of an analogue for semigroups of the so-called Felsch strategy from the Todd-Coxeter algorithm for groups.

This https://arxiv.org/abs/2211.08145 has been replaced.
link: https://scholar.google.com/scholar?q=a

Strong topological Rokhlin property, shadowing, and symbolic dynamics of countable groups
A countable group $G$ has the strong topological Rokhlin property (STRP) if it admits a continuous action on the Cantor space with a comeager conjugacy class. We show that having the STRP is a symbolic dynamical property. We prove that a countable group $G$ has the STRP if and only if certain sofic subshifts over $G$ are dense in the space of subshifts. A sufficient condition is that isolated shifts over $G$ are dense in the space of all subshifts. We provide numerous applications including t…

This https://arxiv.org/abs/2107.07102 has been replaced.
link: https://scholar.google.com/scholar?q=a

A contact McKay correspondence for links of simple singularities
We compute the cylindrical contact homology of the links of the simple singularities. These manifolds are contactomorphic to $S^3/G$ for finite subgroups $G\subset SU(2)$. We perturb the degenerate contact form on $S^3/G$ with a Morse function, which is invariant under the corresponding $H\subset SO(3)$ action on $S^2$, to achieve nondegeneracy up to an action threshold. The cylindrical contact homology is recovered by taking a direct limit of the action filtered homology groups. The ranks of t…

This https://arxiv.org/abs/2307.12833 has been replaced.
link: https://scholar.google.com/scholar?q=a

When can networks be inferred from observed groups?
Collecting network data directly from network members can be challenging. One alternative involves inferring a network from observed groups, for example, inferring a network of scientific collaboration from researchers' observed paper authorships. In this paper, I explore when an unobserved undirected network of interest can accurately be inferred from observed groups. The analysis uses simulations to experimentally manipulate the structure of the unobserved network to be inferred, the number o…

This https://arxiv.org/abs/2105.12081 has been replaced.
link: https://scholar.google.com/scholar?q=a

Group selection and shrinkage: Structured sparsity for semiparametric additive models
Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection. This work introduces structured sparse estimators that combine group subset selection with shrinkage. To accommodate sophisticated structures, our estimators allow for arbitrary overlap between groups. We develop an optimization framework for fitting the nonconv…

At @… we have a list of things we have but don't constantly use that other orgs/groups can borrow from/in our studios in Penryn and Sheffield. Folks rarely take us up on it but here it is. There must be so much underused and dusty equipment in the world.

Interested in San Francisco history? In that case this might be of interest:
Join us in-person or online via Zoom Monday, March 11, 2024 for Empress San Francisco: The Pacific Rim, The Great West, and California at the Panama-Pacific International Exposition
6:00-7:15 PM, see registration links below.
Register to attend in-person:

Empress San Francisco: The Pacific Rim, The Great West, and California at the Panama-Pacific International Exposition
Monday, March 11, 2024 5:30 PM Pacific - Reception 6:00 PM Pacific - Program The Book Club of California | 312 Sutter Street | San Francisco, California 94108 When the more than 18 million visitors poured into the Panama-Pacific International Exposition (PPIE) in San Francisco in 1915, they encountered a vision of the world born out of San Francisco’s particular local political and social climate. By seeking to please various constituent groups ranging from the government of Japan…

Interested in San Francisco history? In that case this might be of interest:
Join us in-person or online via Zoom Monday, March 11, 2024 for Empress San Francisco: The Pacific Rim, The Great West, and California at the Panama-Pacific International Exposition
6:00-7:15 PM, see registration links below.
Register to attend in-person:

Empress San Francisco: The Pacific Rim, The Great West, and California at the Panama-Pacific International Exposition
Monday, March 11, 2024 5:30 PM Pacific - Reception 6:00 PM Pacific - Program The Book Club of California | 312 Sutter Street | San Francisco, California 94108 When the more than 18 million visitors poured into the Panama-Pacific International Exposition (PPIE) in San Francisco in 1915, they encountered a vision of the world born out of San Francisco’s particular local political and social climate. By seeking to please various constituent groups ranging from the government of Japan…

This https://arxiv.org/abs/2112.09975 has been replaced.
link: https://scholar.google.com/scholar?q=a

Algorithm Design: A Fairness-Accuracy Frontier
Algorithm designers increasingly optimize not only for accuracy, but also for the fairness of the algorithm across pre-defined groups. We study the tradeoff between fairness and accuracy for any given set of inputs to the algorithm. We propose and characterize a fairness-accuracy frontier, which consists of the optimal points across a broad range of preferences over fairness and accuracy. Our results identify a simple property of the inputs, group-balance, which qualitatively determines the sha…

@… I remember my first web related project in High School was writing a scraper, and I vividly recall coming across this thing in my research: https://groups.google.com/g/c…

This https://arxiv.org/abs/2211.12971 has been replaced.
link: https://scholar.google.com/scholar?q=a

Cooperative data-driven modeling
Data-driven modeling in mechanics is evolving rapidly based on recent machine learning advances, especially on artificial neural networks. As the field matures, new data and models created by different groups become available, opening possibilities for cooperative modeling. However, artificial neural networks suffer from catastrophic forgetting, i.e. they forget how to perform an old task when trained on a new one. This hinders cooperation because adapting an existing model for a new task affec…

Axel Springer and 31 other media groups in Europe file a $2.3B lawsuit against Google, alleging that they suffered losses due to its digital ad practices (Foo Yun Chee/Reuters)
https://www.reuters.com/technology/google-

This https://arxiv.org/abs/2402.03152 has been replaced.
link: https://scholar.google.com/scholar?q=a

Rational Maps of Balls and their Associated Groups
Given a proper, rational map of balls, D'Angelo and Xiao introduced five natural groups encoding properties of the map. We study these groups using a recently discovered normal form for rational maps of balls. Using this normal form, we also provide several new groups associated to the map.

This https://arxiv.org/abs/2102.07928 has been replaced.
link: https://scholar.google.com/scholar?q=a

Ramification groups of some finite Galois extensions of maximal nilpotency class over local fields of positive characteristic
We examine the ramification groups of finite Galois extensions over complete discrete valuation fields of equal characteristic $p>0$. Brylinski (1983) calculated the ramification groups in the case where the Galois groups are abelian. We extend the results of Brylinski to some non-abelian cases where the Galois groups are of order $\leq p^{p+1}$ and of maximal nilpotency class.

“I think the defining economic reality of the modern platform media world is that all the platforms realized that an infinite supply of teenage creators are cheaper to deal with than media companies or groups of media individuals or powerful creators”
Great interview with @…, very worthwhile and

Decoder guest host Hank Green makes Nilay Patel explain why websites have a future
Complexly co-founder and YouTuber Hank Green guest hosts Decoder to interview Nilay Patel on the future of the web.

This https://arxiv.org/abs/1005.2465 has been replaced.
link: https://scholar.google.com/scholar?q=a<…

Dichotic harmony for the musical practice
The dichotic method of hearing sound adapts in the region of musical harmony. The algorithm of the separation of the being dissonant voices into several separate groups is proposed. For an increase in the pleasantness of chords the different groups of voices are heard out through the different channels of headphones. Is created two demonstration program for PC. Keywords: music, harmony, chord, dichotic listening, dissonance, consonance, headphones, pleasantness, midi.

This https://arxiv.org/abs/2206.05677 has been replaced.
link: https://scholar.google.com/scholar?q=a

On groups interpretable in various valued fields
We study infinite groups interpretable in three families of valued fields: $V$-minimal, power bounded $T$-convex, and $p$-adically closed fields. We show that every such group $G$ has unbounded exponent and that if $G$ is dp-minimal then it is abelian-by-finite. Along the way, we associate with any infinite interpretable group an infinite type-definable subgroup which is definably isomorphic to a group in one of four distinguished sorts: the underlying valued field $K$, its residue field $\ma…

This https://arxiv.org/abs/1905.05867 has been replaced.
link: https://scholar.google.com/scholar?q=a

On Borel subalgebras of quantum groups
For a quantum group, we study those right coideal subalgebras, for which all irreducible representations are one-dimensional. If a right coideal subalgebra is maximal with this property, then we call it a Borel subalgebra. Besides the positive part of the quantum group and its reflections, we find new unfamiliar Borel subalgebras, for example, ones containing copies of the quantum Weyl algebra. Given a Borel subalgebra, we study its induced (Verma-)modules and prove among others that they hav…

This https://arxiv.org/abs/2203.01307 has been replaced.
link: https://scholar.google.com/scholar?q=a

An $L^p$-spectral multiplier theorem with sharp $p$-specific regularity bound on Heisenberg type groups
We prove an $L^p$-spectral multiplier theorem for sub-Laplacians on Heisenberg type groups under the sharp regularity condition $s>d\left|1/p-1/2\right|$, where $d$ is the topological dimension of the underlying group. Our approach relies on restriction type estimates where the multiplier is additionally truncated along the spectrum of the Laplacian on the center of the group.

Axel Springer and 31 other media groups in Europe file a $2.3B lawsuit against Google, alleging that they suffered losses due to its digital ad practices (Foo Yun Chee/Reuters)
https://www.reuters.com/technology/google-

This https://arxiv.org/abs/2403.01658 has been replaced.
link: https://scholar.google.com/scholar?q=a

Noise sensitivity and stability on groups
We discuss finitely generated infinite groups on which natural random walks are noise sensitive in total variation as well as ones on which natural random walks are noise stable in total variation.

This https://arxiv.org/abs/2201.10539 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the intersection of local Arthur packets for classical groups and applications
In this paper, for symplectic and split odd special orthogonal groups, we develop an account of theory on the intersection problem of local Arthur packets. Specifically, following Atobe's reformulation on Mœglin's construction of local Arthur packets, we give a complete set of operators on the construction data, based on which, we provide algorithms and Sage codes to determine whether a given representation is of Arthur type. Furthermore, for any representation $π$ of Arthur type, we give a p…

ICYMI, Chrome has said it intends to prototype the CSS property `reading-order-items`:
https://groups.google.com/a/chromium.org/g/blink-dev/c/d9jIhcVw8zQ/m/aM5d-3P7AQAJ
If this is new to you, I cover the broad challenges with readi…

Is there an alternative to Google Groups that has reasonable pricing, unlike Groups.io, and that's exclusively a normal mailing list without bells and whistles?
#AskFedi #MailingLists #Mailman

This https://arxiv.org/abs/1812.08946 has been replaced.
link: https://scholar.google.com/scholar?q=a

Lectures on 4d N=1 dynamics and related topics
This lecture series consists of mostly independent three parts: Part 1: a tour of basic 4d N=1 supersymmetric dynamics, covering the pure super Yang-Mills, the Seiberg duality for classical groups, the supersymmetric index on S^3, and the a-maximization. Part 2: a brief look at 2d N=(2,2) and N=(0,2) dynamics, covering the Landau-Ginzburg and Calabi-Yau models, the elliptic genera on T^2, and the triality of Gadde-Gukov-Putrov. Appendix: a review of basic properties of supersymmetries in variou…

This https://arxiv.org/abs/2210.15229 has been replaced.
link: https://scholar.google.com/scholar?q=a

On Chow groups of toric schemes over a DVR
We give an explicit combinatorial presentation of the Chow groups of a toric scheme over a DVR. As an application, we compute the Chow groups of several toric schemes over a DVR and of their special fibers.

A comparison of online search engine autocompletion in Google and Baidu
Geng Liu, Pietro Pinoli, Stefano Ceri, Francesco Pierri
https://arxiv.org/abs/2405.01917

A comparison of online search engine autocompletion in Google and Baidu
Warning: This paper contains content that may be offensive or upsetting. Online search engine auto-completions make it faster for users to search and access information. However, they also have the potential to reinforce and promote stereotypes and negative opinions about a variety of social groups. We study the characteristics of search auto-completions in two different linguistic and cultural contexts: Baidu and Google. We find differences between the two search engines in the way they suppre…

This https://arxiv.org/abs/2203.06868 has been replaced.
link: https://scholar.google.com/scholar?q=a

Topological asymptotic dimension
We initiate a study of asymptotic dimension for locally compact groups. This notion extends the existing invariant for discrete groups and is shown to be finite for a large class of residually compact groups. Along the way, the notion of Hirsch length is extended to topological groups and classical results of Hirsch and Malcev are extended using a topological version of the Poincaré lemma. We show that polycyclic-by-compact groups and compactly generated, topologically virtually nilpotent grou…

This https://arxiv.org/abs/2205.01426 has been replaced.
link: https://scholar.google.com/scholar?q=a

Extreme Values of Permutation Statistics
We investigate extreme values of Mahonian and Eulerian distributions arising from counting inversions and descents of random elements of finite Coxeter groups. To this end, we construct a triangular array of either distribution from a sequence of Coxeter groups with increasing ranks. To avoid degeneracy of extreme values, the number of i.i.d. samples $k_n$ in each row must be asymptotically bounded. We employ large deviations theory to prove the Gumbel attraction of Mahonian and Eulerian distri…

This https://arxiv.org/abs/2107.13509 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Who in XAI: How AI Background Shapes Perceptions of AI Explanations
Explainability of AI systems is critical for users to take informed actions. Understanding "who" opens the black-box of AI is just as important as opening it. We conduct a mixed-methods study of how two different groups--people with and without AI background--perceive different types of AI explanations. Quantitatively, we share user perceptions along five dimensions. Qualitatively, we describe how AI background can influence interpretations, elucidating the differences through lenses of appropr…

The root of the problem here is, of course, pretending that the output of generative #AI is actually *meaningful*, when in fact it’s a guided extrapolation of the training set. You can’t blanket prompt-engineer your way out of a biased training set, because you’ll simply flip the teeter-totter the other way, as we see here.
It’s pretty clear that Google’s canned prompt includes something like “depi…

Google apologizes for ‘missing the mark’ after Gemini generated racially diverse Nazis
Google says it’s aware of historically inaccurate results for its Gemini AI image generator, following criticism that it depicted historically white groups as people of color.

This https://arxiv.org/abs/2310.18553 has been replaced.
link: https://scholar.google.com/scholar?q=a

Affective Polarization and Dynamics of Information Spread in Online Networks
Members of different political groups not only disagree about issues but also dislike and distrust each other. While social media can amplify this emotional divide -- called affective polarization by political scientists -- there is a lack of agreement on its strength and prevalence. We measure affective polarization on social media by quantifying the emotions and toxicity of reply interactions. We demonstrate that, as predicted by affective polarization, interactions between users with same id…

This https://arxiv.org/abs/2401.08495 has been replaced.
link: https://scholar.google.com/scholar?q=a

Large Language Models Portray Socially Subordinate Groups as More Homogeneous, Consistent with a Bias Observed in Humans
Large language models (LLMs) are becoming pervasive in everyday life, yet their propensity to reproduce biases inherited from training data remains a pressing concern. Prior investigations into bias in LLMs have focused on the association of social groups with stereotypical attributes. However, this is only one form of human bias such systems may reproduce. We investigate a new form of bias in LLMs that resembles a social psychological phenomenon where socially subordinate groups are perceived …

This https://arxiv.org/abs/2211.13913 has been replaced.
link: https://scholar.google.com/scholar?q=a

Constants for Artin like problems in Kummer and division fields
We apply the character sums method of Lenstra, Moree, and Stevenhagen, to explicitly compute the constants in the Titchmarsh divisor problem for Kummer fields and for division fields of Serre curves. We derive our results as special cases of a general result on the product expressions for the sums in the form $$\sum_{n=1}^{\infty}\frac{g(n)}{\#G(n)}$$ in which $g(n)$ is a multiplicative arithmetic function and $\{G(n)\}$ is a certain family of Galois groups. Our results extend the application o…

This https://arxiv.org/abs/2110.11655 has been replaced.
link: https://scholar.google.com/scholar?q=a

Parafree graphs of groups with cyclic edge groups
We establish a combination theorem for parafree groups. These groups were introduced by Baumslag in the sixties. One of the current motivations for a better understanding of their structure is that they show up naturally in connection with Remeslennikov's conjecture on the profinite rigidity of free groups. In this article, we determine when the fundamental group of a finite graph of groups with cyclic edge groups is parafree.

This https://arxiv.org/abs/2201.10507 has been replaced.
link: https://scholar.google.com/scholar?q=a

Homological Lagrangian monodromy for some monotone tori
Given a Lagrangian submanifold $L$ in a symplectic manifold $X$, the homological Lagrangian monodromy group $\mathcal{H}_L$ describes how Hamiltonian diffeomorphisms of $X$ preserving $L$ setwise act on $H_*(L)$. We begin a systematic study of this group when $L$ is a monotone Lagrangian $n$-torus. Among other things, we describe $\mathcal{H}_L$ completely when $L$ is a monotone toric fibre, make significant progress towards classifying the groups than can occur for $n=2$, and make a conjecture…

This https://arxiv.org/abs/2206.06344 has been replaced.
link: https://scholar.google.com/scholar?q=a

Sparse-group boosting -- Unbiased group and variable selection
In the presence of grouped covariates, we propose a framework for boosting that allows to enforce sparsity within and between groups. By using component-wise and group-wise gradient boosting at the same time with adjusted degrees of freedom, a model with similar properties as the sparse group lasso can be fitted through boosting. We show that within-group and between-group sparsity can be controlled by a mixing parameter and discuss similarities and differences to the mixing parameter in the sp…

This https://arxiv.org/abs/2402.00158 has been replaced.
link: https://scholar.google.com/scholar?q=a

Zero fibers of quaternionic quotient singularities
We propose a generalization of Haiman's conjecture on the diagonal coinvariant rings of real reflection groups to the context of irreducible quaternionic reflection groups (also known as symplectic reflection groups). For a reflection group $W$ acting on a quaternionic vector space $V$, by regarding $V$ as a complex vector space we consider the scheme-theoretic fiber over zero of the quotient map $π:V \to V/W$. For $W$ an irreducible reflection group of (quaternionic) rank at least $6$, we sho…

This https://arxiv.org/abs/2208.10114 has been replaced.
link: https://scholar.google.com/scholar?q=a

Generalizing Lusztig's total positivity
We introduce the notion of $Θ$-positivity in real simple Lie groups. This notion at the same time generalizes Lusztig's total positivity in split real Lie groups and invariant orders in Lie groups of Hermitian type. We show that there are four families of Lie groups which admit $Θ$-positive structures, and investigate basic properties of $Θ$-positivity.

This https://arxiv.org/abs/2111.00685 has been replaced.
link: https://scholar.google.com/scholar?q=a

Extensions of Veech groups II: Hierarchical hyperbolicity and quasi-isometric rigidity
We show that for any lattice Veech group in the mapping class group $\mathrm{Mod}(S)$ of a closed surface $S$, the associated $π_1 S$--extension group is a hierarchically hyperbolic group. As a consequence, we prove that any such extension group is quasi-isometrically rigid.

This https://arxiv.org/abs/2402.00595 has been replaced.
link: https://scholar.google.com/scholar?q=a

Causal evidence for social group sizes from Wikipedia editing data
Human communities have self-organizing properties in which specific Dunbar Numbers may be invoked to explain group attachments. By analyzing Wikipedia editing histories across a wide range of subject pages, we show that there is an emergent coherence in the size of transient groups formed to edit the content of subject texts, with two peaks averaging at around $N=8$ for the size corresponding to maximal contention, and at around $N=4$ as a regular team. These values are consistent with the obse…

This https://arxiv.org/abs/2004.03587 has been replaced.
link: https://scholar.google.com/scholar?q=a

Good Basic Invariants for Elliptic Weyl Groups and Frobenius Structures
In this paper, we define a set of good basic invariants for the elliptic Weyl group for the elliptic root system. For an elliptic root system of codimension $1$, we show that a set of good basic invariants gives a set of flat invariants obtained by Saito and Taylor coefficients of the good basic invariants give the structure constants of the multiplication of the Frobenius structure obtained by the author.

This https://arxiv.org/abs/2110.11655 has been replaced.
link: https://scholar.google.com/scholar?q=a

Parafree graphs of groups with cyclic edge groups
We establish a combination theorem for parafree groups. These groups were introduced by Baumslag in the sixties. One of the current motivations for a better understanding of their structure is that they show up naturally in connection with Remeslennikov's conjecture on the profinite rigidity of free groups. In this article, we determine when the fundamental group of a finite graph of groups with cyclic edge groups is parafree.

This https://arxiv.org/abs/2208.05316 has been replaced.
link: https://scholar.google.com/scholar?q=a

Welfare ordering of voting weight allocations
This paper studies the allocation of voting weights in a committee representing groups of different sizes. We introduce a partial ordering of weight allocations based on stochastic comparison of social welfare. We show that when the number of groups is sufficiently large, this ordering asymptotically coincides with the total ordering induced by the cosine proportionality between the weights and the group sizes. A corollary is that a class of expectation-form objective functions, including expec…

This https://arxiv.org/abs/2006.16425 has been replaced.
link: https://scholar.google.com/scholar?q=a

Extensions of Veech groups I: A hyperbolic action
Given a lattice Veech group in the mapping class group of a closed surface $S$, this paper investigates the geometry of $Γ$, the associated $π_1S$--extension group. We prove that $Γ$ is the fundamental group of a bundle with a singular Euclidean-by-hyperbolic geometry. Our main result is that collapsing "obvious" product regions of the universal cover produces an action of $Γ$ on a hyperbolic space, retaining most of the geometry of $Γ$. This action is a key ingredient in the sequel where …

This https://arxiv.org/abs/2209.03816 has been replaced.
link: https://scholar.google.com/scholar?q=a

The closure ordering conjecture on local Arthur packets of classical groups
In this paper, we prove the closure ordering conjecture on the local $L$-parameters of representations in local Arthur packets of $\mathrm{G}_n=\mathrm{Sp}_{2n}, \mathrm{SO}_{2n+1}$ over a non-Archimedean local field of characteristic zero. Precisely, given any representation $π$ in a local Arthur packet $Π_ψ$, the closure of the local $L$-parameter of $π$ in the Vogan variety must contain the local $L$-parameter corresponding to $ψ$. This conjecture reveals a geometric nature of local Art…

This https://arxiv.org/abs/2209.00580 has been replaced.
link: https://scholar.google.com/scholar?q=a

Soficity, Amenability, and LEF-ness for topological full groups
In this paper, we study several finite approximation properties of topological full groups of group actions on the Cantor set such that free points are dense. Firstly, we establish that for such a distal action $α$ of a countable discrete group $G$ on the Cantor set, the topological full group $[[α]]$ is amenable if and only if $G$ is amenable. This result is obtained through a novel method that detects hyperfiniteness in certain sofic approximation graph sequences of finitely generated subgr…

Finding the white male: The prevalence and consequences of algorithmic gender and race bias in political Google searches
Tobias Rohrbach, Mykola Makhortykh, Maryna Sydorova
https://arxiv.org/abs/2405.00335

Finding the white male: The prevalence and consequences of algorithmic gender and race bias in political Google searches
Search engines like Google have become major information gatekeepers that use artificial intelligence (AI) to determine who and what voters find when searching for political information. This article proposes and tests a framework of algorithmic representation of minoritized groups in a series of four studies. First, two algorithm audits of political image searches delineate how search engines reflect and uphold structural inequalities by under- and misrepresenting women and non-white politicia…

This https://arxiv.org/abs/2211.15575 has been replaced.
link: https://scholar.google.com/scholar?q=a

Hyperbolicity and bounded-valued cohomology
We generalise a theorem of Gersten on surjectivity of the restriction map in $\ell^{\infty}$-cohomology of groups. This leads to applications on subgroups of hyperbolic groups, quasi-isometric distinction of finitely generated groups and $\ell^{\infty}$-cohomology calculations for some well-known classes of groups. Along the way, we obtain hyperbolicity criteria for groups of type $FP_2(\mathbb Q)$ and for those satisfying a rational homological linear isoperimetric inequality, answering a ques…

This https://arxiv.org/abs/2105.11359 has been replaced.
link: https://scholar.google.com/scholar?q=a

Examples of measures with trivial left and non-trivial right random walk tail boundary
In early 80's Vadim Kaimanovich presented a construction of a non-degenerate measure, on the standard lamplighter group, that has a trivial left and non-trivial right random walk tail boundary. We show that examples of such kind are possible precisely for amenable groups that have non-trivial factors with infinite conjugacy classes property.

This https://arxiv.org/abs/2402.01189 has been replaced.
link: https://scholar.google.com/scholar?q=a

On Malle's conjecture for the product of symmetric and nilpotent groups
Let $G$ be a finite nilpotent group and $n\in \{3,4, 5\}$. Consider $S_n\times G$ as a subgroup of $S_n\times S_{|G|}\subset S_{n|G|}$, where $G$ embeds into the second factor of $S_n\times S_{|G|}$ via the regular representation. Over any number field $k$, we prove the strong form of Malle's conjecture for $S_n\times G$ viewed as a subgroup of $S_{n|G|}$. Our result requires that $G$ satisfies some mild conditions.

This https://arxiv.org/abs/2210.07515 has been replaced.
link: https://scholar.google.com/scholar?q=a

CR embeddings of nilpotent Lie groups
We show that a connected, simply connected nilpotent Lie group with an integrable left-invariant complex structure on a generating and suitably complemented subbundle of the tangent bundle admits a CR embedding in complex space as the edge of a wedge in a complex domain defined by polynomials.

The EU opens formal DMA investigations into Apple and Google over letting developers "steer" users from their app stores, and Meta over using user data for ads (Javier Espinoza/Financial Times)
https://t.co/BtANTE4Le6

This https://arxiv.org/abs/2403.01541 has been replaced.
link: https://scholar.google.com/scholar?q=a

Reversibility in the Seifert-fibered spaces
An element $a$ in a group $Γ$ is called \emph{reversible} if there exists $g \in Γ$ such that $gag^{-1}=a^{-1}$. The reversible elements are also known as `real elements' or `reciprocal elements' in literature. In this paper, we classify the reversible elements in Fuchsian groups, and use this classification to find all reversible elements in a Seifert-fibered group. In the last section we apply this classification to the braid groups, particularly to the braid group on $3$ strands.

This https://arxiv.org/abs/2402.03450 has been replaced.
link: https://scholar.google.com/scholar?q=a

Recommendation Fairness in Social Networks Over Time
In social recommender systems, it is crucial that the recommendation models provide equitable visibility for different demographic groups, such as gender or race. Most existing research has addressed this problem by only studying individual static snapshots of networks that typically change over time. To address this gap, we study the evolution of recommendation fairness over time and its relation to dynamic network properties. We examine three real-world dynamic networks by evaluating the fair…

This https://arxiv.org/abs/2012.09323 has been replaced.
link: https://scholar.google.com/scholar?q=a

Simple modules of small quantum groups at dihedral groups
Based on previous results on the classification of finite-dimensional Nichols algebras over dihedral groups and the characterization of simple modules of Drinfeld doubles, we compute the irreducible characters of the Drinfeld doubles of bosonizations of finite-dimensional Nichols algebras over the dihedral groups $\mathbb{D}_{4t}$ with $t\geq 3$. To this end, we develop new techniques that can be applied to Nichols algebras over any Hopf algebra. Namely, we explain how to construct recursively …

This https://arxiv.org/abs/2402.04592 has been replaced.
link: https://scholar.google.com/scholar?q=a

Frattini subgroups of hyperbolic-like groups
We study Frattini subgroups of various generalizations of hyperbolic groups. For any countable group $G$ admitting a general type action on a hyperbolic space $S$, we show that the induced action of the Frattini subgroup $Φ(G)$ on $S$ has bounded orbits. This implies that $Φ(G)$ is "small" compared to $G$; in particular, $|G:Φ(G)|=\infty$. In contrast, for any finitely generated non-cyclic group $Q$ with $Φ(Q)=\{ 1\}$, we construct an infinite lacunary hyperbolic group $L$ such th…

This https://arxiv.org/abs/2403.01541 has been replaced.
link: https://scholar.google.com/scholar?q=a

Reversibility in the Seifert-fibered spaces
An element $a$ in a group $Γ$ is called \emph{reversible} if there exists $g \in Γ$ such that $gag^{-1}=a^{-1}$. The reversible elements are also known as `real elements' or `reciprocal elements' in literature. In this paper, we classify the reversible elements in Fuchsian groups, and use this classification to find all reversible elements in a Seifert-fibered group. In the last section we apply this classification to the braid groups, particularly to the braid group on $3$ strands.

This https://arxiv.org/abs/2204.08053 has been replaced.
link: https://scholar.google.com/scholar?q=a

Automorphic Forms on Unitary Groups
This manuscript provides a more detailed treatment of the material from my lecture series at the 2022 Arizona Winter School on Automorphic Forms Beyond $GL_2$. The main focus of this manuscript is automorphic forms on unitary groups, with a view toward algebraicity results. I also discuss related aspects of automorphic $L$-functions in the setting of unitary groups.

Finding the white male: The prevalence and consequences of algorithmic gender and race bias in political Google searches
Tobias Rohrbach, Mykola Makhortykh, Maryna Sydorova
https://arxiv.org/abs/2405.00335

Finding the white male: The prevalence and consequences of algorithmic gender and race bias in political Google searches
Search engines like Google have become major information gatekeepers that use artificial intelligence (AI) to determine who and what voters find when searching for political information. This article proposes and tests a framework of algorithmic representation of minoritized groups in a series of four studies. First, two algorithm audits of political image searches delineate how search engines reflect and uphold structural inequalities by under- and misrepresenting women and non-white politicia…

This https://arxiv.org/abs/2205.13991 has been replaced.
link: https://scholar.google.com/scholar?q=a

Algebraic fundamental groups of fake projective planes
Fundamental groups of fake projective planes fall into fifty distinct isomorphism classes, one for each complex conjugate pair. We prove that this is not the case for their algebraic fundamental groups: there are only forty-six isomorphism classes. We show that there are four pairs of complex conjugate pairs of fake projective planes that are $\mathrm{Aut}(\mathbb{C})$-equivalent and hence have mutually isomorphic algebraic fundamental groups. All other pairs of algebraic fundamental groups are…

This https://arxiv.org/abs/2205.06692 has been replaced.
link: https://scholar.google.com/scholar?q=a

Co-spectral radius for countable equivalence relations
We define the co-spectral radius of inclusions $\mathcal{S}\leq \mathcal{R}$ of discrete, probability measure-preserving equivalence relations, as the sampling exponent of a generating random walk on the ambient relation. The co-spectral radius is analogous to the spectral radius for random walks on $G/H$ for inclusion $H\leq G$ of groups. For the proof, we develop a more general version of the 2-3 method we used in another work on the growth of unimodular random rooted trees. We use this metho…

This https://arxiv.org/abs/2204.08053 has been replaced.
link: https://scholar.google.com/scholar?q=a

Automorphic Forms on Unitary Groups
This manuscript provides a more detailed treatment of the material from my lecture series at the 2022 Arizona Winter School on Automorphic Forms Beyond $GL_2$. The main focus of this manuscript is automorphic forms on unitary groups, with a view toward algebraicity results. I also discuss related aspects of automorphic $L$-functions in the setting of unitary groups.

Meta, Google, OpenAI, child safety group Thorn, nonprofit All Tech Is Human, and other AI groups sign on to an initiative to add new child safety measures (Deepa Seetharaman/Wall Street Journal)
https://www.wsj.com/tech/ai/ai-developers-

This https://arxiv.org/abs/2203.01483 has been replaced.
link: https://scholar.google.com/scholar?q=a

Constitutional Implementation of Affirmative Action Policies in India
India is home to a comprehensive affirmative action program that reserves a fraction of positions at governmental institutions for various disadvantaged groups. While there is a Supreme Court-endorsed mechanism to implement these reservation policies when all positions are identical, courts have refrained from endorsing explicit mechanisms when positions are heterogeneous. This lacunae has resulted in widespread adoption of unconstitutional mechanisms, countless lawsuits, and inconsistent court…

This https://arxiv.org/abs/2207.03659 has been replaced.
link: https://scholar.google.com/scholar?q=a

$Out(F_n)$-invariant probability measures on the space of $n$-generated marked groups
Let $\mathcal G_n$ denote the space of $n$-generated marked groups. We prove that, for every $n\ge 2$, there exist $2^{\aleph_0}$ non-atomic, $Out(F_n)$-invariant, mixing probability measures on $\mathcal G_n$. On the other hand, there are non-empty closed subsets of $\mathcal G_n$ that admit no $Out(F_n)$-invariant probability measure. Acylindrical hyperbolicity of the group $Aut(F_n)$ plays a crucial role in the proof of both results. We also discuss model theoretic implications of the existe…

This https://arxiv.org/abs/2112.10830 has been replaced.
link: https://scholar.google.com/scholar?q=a

Nonabelian Hodge theory for stacks and a stacky P=W conjecture
We introduce a version of the P=W conjecture relating the Borel-Moore homology of the stack of representations of the fundamental group of a genus g Riemann surface with the Borel-Moore homology of the stack of degree zero semistable Higgs bundles on a smooth projective complex curve of genus $g$. In order to state the conjecture we propose a construction of a canonical isomorphism between these Borel-Moore homology groups. We relate the stacky P=W conjecture with the original P=W conjecture co…

This https://arxiv.org/abs/2101.02732 has been replaced.
link: https://scholar.google.com/scholar?q=a

Reality of Unipotent elements in Classical Lie Groups
The aim of this paper is to give a classification of real and strongly real unipotent elements in a classical simple Lie group. To do this, we will introduce an infinitesimal version of the notion of classical reality in a Lie group. This notion has been applied to classify real and strongly real unipotent elements in a classical simple Lie group.

Sources: Biden administration is encouraging US tech groups to seek AI deals in the UAE and brokered Microsoft's deal with G42, as it seeks an edge over China (Financial Times)
https://t.co/9FSdsEjV0t

This https://arxiv.org/abs/2404.00663 has been replaced.
link: https://scholar.google.com/scholar?q=a

Geometrizations of quantum groups and dual semicanonical bases
In this paper, we give a geometrization of semicanonical bases of quantum groups via Grothendieck groups of the derived categories of Lusztig's nilpotent varieties. Meanwhile, we describe the dual semicanonical bases in terms of Serre polynomials of Grassmannians of modules over preprojective algebras.

This https://arxiv.org/abs/2203.16234 has been replaced.
link: https://scholar.google.com/scholar?q=a

An analytic viewpoint on the Hasse principle
Working on Berkovich analytic curves, we propose a geometric approach to the study of the Hasse principle over function fields of curves defined over a complete discretely valued field. Using it, we show the Hasse principle to be verified for certain families of projective homogeneous spaces. As a consequence, we also obtain said principle in the already known cases of quadratic forms and homogeneous varieties over unitary groups.

This https://arxiv.org/abs/2208.11938 has been replaced.
link: https://scholar.google.com/scholar?q=a

Parabolic subgroups of complex braid groups
In this paper we introduce a class of `parabolic' subgroups for the generalized braid group associated to an arbitrary irreducible complex reflection group, which maps onto the collection of parabolic subgroups of the reflection group. Except for one case, which is proven separately elsewhere, we prove that this collection forms a lattice, so that intersections of parabolic subgroups are parabolic subgroups. In particular, every element admits a parabolic closure, which is the smallest paraboli…

This https://arxiv.org/abs/2005.11533 has been replaced.
link: https://scholar.google.com/scholar?q=a

Arakelov class groups of random number fields
The main purpose of the paper is to formulate a probabilistic model for Arakelov class groups in families of number fields, offering a correction to the Cohen--Lenstra--Martinet heuristic on ideal class groups. To that end, we show that Chinburg's Omega(3) conjecture implies tight restrictions on the Galois module structure of oriented Arakelov class groups. As a consequence, we construct a new infinite series of counterexamples to the Cohen--Lenstra--Martinet heuristic, which have the novel fe…

This https://arxiv.org/abs/2201.01790 has been replaced.
link: https://scholar.google.com/scholar?q=a

Exotic Fusion Systems Related to Sporadic Simple Groups (Version With Code)
We describe several exotic fusion systems related to the Sporadic simple groups at odd primes. More generally, we classify saturated fusion systems supported on Sylow $3$-subgroups of the Conway group $\mathrm{Co}_1$ and the Thompson group $\mathrm{F}_3$, and a Sylow $5$-subgroup of the Monster $\mathrm{M}$, as well as a particular maximal subgroup of the latter two $p$-groups. This work is supported by computations in MAGMA.

This https://arxiv.org/abs/2212.12225 has been replaced.
link: https://scholar.google.com/scholar?q=a

Hyperbolicity and fundamental groups of complex quasi-projective varieties
This paper investigates the relationship between the hyperbolicity of complex quasi-projective varieties $X$ and the (topological) fundamental group $π_1(X)$ in the presence of a linear representation $\varrho: π_1(X) \to {\rm GL}_N(\mathbb{C})$. We present our main results in three parts. Firstly, we show that if $\varrho$ is bigand the Zariski closure of $\varrho(π_1(X))$ semisimple, then for any $X^σ:=X\times_σ\mathbb{C}$ where $σ\in {\rm Aut}(\mathbb{C}/\mathbb{Q})$, there exists a …

This https://arxiv.org/abs/2204.01945 has been replaced.
link: https://scholar.google.com/scholar?q=a

Mapping class groups of manifolds with boundary are of finite type
In this note we prove that the mapping class group of a compact topological manifold $M$ with boundary is of finite type, under assumptions on its dimension and connectivity.

This https://arxiv.org/abs/2201.01790 has been replaced.
link: https://scholar.google.com/scholar?q=a

Exotic Fusion Systems Related to Sporadic Simple Groups (Version With Code)
We describe several exotic fusion systems related to the Sporadic simple groups at odd primes. More generally, we classify saturated fusion systems supported on Sylow $3$-subgroups of the Conway group $\mathrm{Co}_1$ and the Thompson group $\mathrm{F}_3$, and a Sylow $5$-subgroup of the Monster $\mathrm{M}$, as well as a particular maximal subgroup of the latter two $p$-groups. This work is supported by computations in MAGMA.

This https://arxiv.org/abs/1909.09832 has been replaced.
link: https://scholar.google.com/scholar?q=a

Upper Ramification Groups for Arbitrary Valuation Rings
T. Saito established a ramification theory for ring extensions locally of complete intersection. We show that for a Henselian valuation ring $A$ with field of fractions $K$ and for a finite Galois extension $L$ of $K$, the integral closure $B$ of $A$ in $L$ is a filtered union of subrings of $B$ which are of complete intersection over $A$. By this, we can obtain a ramification theory of Henselian valuation rings as the limit of the ramification theory of Saito. Our theory generalizes the ramifi…

This https://arxiv.org/abs/2212.01993 has been replaced.
link: https://scholar.google.com/scholar?q=a

Forest-skein groups II: construction from homogeneously presented monoids
Inspired by the reconstruction program of conformal field theories of Vaughan Jones we recently introduced a vast class of so called forest-skein groups. They are built from a skein presentation: a set of colours and a set of pairs of coloured trees. Each nice skein presentation produces four groups similar to Richard Thompson's group F,T,V and the braided version BV of Brin and Dehornoy. In this article, we consider forest-skein groups obtained from one-dimensional skein presentations; the d…

This https://arxiv.org/abs/2012.13373 has been replaced.
link: https://scholar.google.com/scholar?q=a

Symmetric and Kähler--Einstein Fano polygons
We investigate singular symmetric and Kähler--Einstein Fano polytopes. In particular we study the automorphism groups of symmetric and Kähler--Einstein Fano polygons in detail.

This https://arxiv.org/abs/1103.5906 has been replaced.
link: https://scholar.google.com/scholar?q=a<…

Torsion groups of elliptic curves over quadratic fields
We describe methods to determine all the possible torsion groups of an elliptic curve that actually appear over a fixed quadratic field. We use these methods to find, for each group that can appear over a quadratic field, the field with the smallest absolute value of it's discriminant such that there exists an elliptic curve with that torsion. We also examine the interplay of the torsion and rank over a fixed quadratic field and see that what happens is very different than over $\Q$. Finally we…

This https://arxiv.org/abs/2012.13373 has been replaced.
link: https://scholar.google.com/scholar?q=a

Symmetric and Kähler--Einstein Fano polygons
We investigate singular symmetric and Kähler--Einstein Fano polytopes. In particular we study the automorphism groups of symmetric and Kähler--Einstein Fano polygons in detail.

This https://arxiv.org/abs/2403.02197 has been replaced.
link: https://scholar.google.com/scholar?q=a

Solvable and non-solvable finite groups of the same order type
We construct two finite groups of size $2^{365}\cdot 3^{105}\cdot 7^{104}$: a solvable group $G$ and a non-solvable group $H$, such that for every integer $n$ the groups have the same number of elements of order $n$. This answers a question posed in 1987 by John G. Thompson.

This https://arxiv.org/abs/1703.06089 has been replaced.
link: https://scholar.google.com/scholar?q=a

Hasse-Minkowski theorem for quadratic forms on groups
We discuss generalizations of the classic Hasse-Minkowski theorem for integral quadratic forms, to quadratic forms over a family of groups, equipped with systems of reduction maps. This family embraces very interesting classes, like Mordell-Weil groups of abelian varieties over number fields, odd algebraic K-theory groups of number fields, and finitely generated subgroups of the multiplicative groups of number fields.

This https://arxiv.org/abs/2004.13206 has been replaced.
link: https://scholar.google.com/scholar?q=a

Graphical splittings of Artin kernels
We study Artin kernels, i.e. kernels of discrete characters of right-angled Artin groups, and we show that they decompose as graphs of groups in a way that can be explicitly computed from the underlying graph. When the underlying graph is chordal we show that every such subgroup either surjects to an infinitely generated free group or is a generalized Baumslag-Solitar group of variable rank. In particular for block graphs (e.g. trees), we obtain an explicit rank formula, and discuss some featur…

This https://arxiv.org/abs/2207.13193 has been replaced.
link: https://scholar.google.com/scholar?q=a

Compatibility of the Fargues--Scholze correspondence for unitary groups
We study unramified unitary and unitary similitude groups in an odd number of variables. Using work of the first and third named authors on the Kottwitz Conjecture for the similitude groups, we show that the Fargues--Scholze local Langlands correspondence agrees with the semi-simplification of the local Langlands correspondences constructed by Mok for the groups we consider. This compatibility result is then combined with the spectral action constructed by Fargues--Scholze, to verify their cate…

This https://arxiv.org/abs/2212.01616 has been replaced.
link: https://scholar.google.com/scholar?q=a

The non-commuting, non-generating graph of a finite simple group
Let $G$ be a group such that $G/Z(G)$ is finite and simple. The non-commuting, non-generating graph $Ξ(G)$ of $G$ has vertex set $G \setminus Z(G)$, with edges corresponding to pairs of elements that do not commute and do not generate $G$. We show that $Ξ(G)$ is connected with diameter at most $5$, with smaller upper bounds for certain families of groups. When $G$ itself is simple, we prove that the diameter of the complement of the generating graph of $G$ has a tight upper bound of $4$. In t…

This https://arxiv.org/abs/2207.04235 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Class of Rearrangement Groups that are not Invariably Generated
A group $G$ is invariably generated if there exists a subset $S \subseteq G$ such that, for every choice $g_s \in G$ for $s \in S$, the group $G$ is generated by $\{ s^{g_s} \mid s \in S \}$. In [GGJ16] Gelander, Golan and Juschenko showed that Thompson groups $T$ and $V$ are not invariably generated. Here we generalize this result to the larger setting of rearrangement groups, proving that any subgroup of a rearrangement group that has a certain transitive property is not invariably generated.

This https://arxiv.org/abs/2210.14990 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the space of subgroups of Baumslag-Solitar groups I: perfect kernel and phenotype
Given a Baumslag-Solitar group, we study its space of subgroups from a topological and dynamical perspective. We first determine its perfect kernel (the largest closed subset without isolated points). We then bring to light a natural partition of the space of subgroups into one closed subset and countably many open subsets that are invariant under the action by conjugation. One of our main results is that the restriction of the action to each piece is topologically transitive. This partition is…

This https://arxiv.org/abs/2202.04060 has been replaced.
link: https://scholar.google.com/scholar?q=a

Streaming word problems
We study deterministic and randomized streaming algorithms for word problems of finitely generated groups. For finitely generated linear groups, metabelian groups and free solvable groups we show the existence of randomized streaming algorithms with logarithmic space complexity for their word problems. We also show that the class of finitely generated groups with a logspace randomized streaming algorithm for the word problem is closed under several group theoretical constructions: finite extens…

This https://arxiv.org/abs/2212.04204 has been replaced.
link: https://scholar.google.com/scholar?q=a

Maximal subgroups of finitely presented special inverse monoids
We study the maximal subgroups (also known as group $\mathcal{H}$-classes) of finitely presented special inverse monoids. We show that the maximal subgroups which can arise in such monoids are exactly the recursively presented groups, and moreover every such maximal subgroup can also arise in the $E$-unitary case. We also prove that the possible groups of units are exactly the finitely generated recursively presented groups; this improves upon a result of, and answers a question of, the first a…

This https://arxiv.org/abs/2011.13016 has been replaced.
link: https://scholar.google.com/scholar?q=a

Finite $2$-groups with exactly three automorphism orbits
We give a complete classification of the finite $2$-groups $G$ for which the automorphism group $\operatorname{Aut}(G)$ acting naturally on $G$ has three orbits. There are two infinite families and one additional group, of order $2^9$. All of them are Suzuki $2$-groups, and they appear in an earlier classification of Dornhoff.

This https://arxiv.org/abs/2012.00427 has been replaced.
link: https://scholar.google.com/scholar?q=a

Special affine representations for hyperbolic groups
In this paper we extend the construction of special representations to Gromov hyperbolic groups which admits complementary series. We prove that these representations have a natural non-trivial reduced cohomology class $[c]$. An analogue of Kuhn-Vershik's formula is established and as a by-product a characterisation of hyperbolic groups that admit complementary series. Investigating dynamical properties of the cohomology class $[c]$ we prove an cocycle equidistribution theorem á la Roblin-Marg…