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Sums of Reciprocals of Fractional Parts and Multiplicative Diophantine Approximation
There are two main interrelated goals of this paper. Firstly we investigate the sums
eBook
The psychology of conspiracy theories
Who believes in conspiracy theories, and why are some people more susceptible to them than others? What are the consequences of such beliefs? Has a conspiracy theory ever turned out to be true? The Psychology of Conspiracy Theories debunks the myth that conspiracy theories are a modern phenomenon, exploring their broad social contexts, from politics to the workplace. The book explains why some people are more susceptible to these beliefs than others and how they are produced by recognizable and predictable psychological processes. Featuring examples such as the 9/11 terrorist attacks and climate change, The Psychology of Conspiracy Theories shows us that while such beliefs are not always irrational and are not a pathological trait, they can be harmful to individuals and society.
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Spectral Properties of Ruelle Transfer Operators for Regular Gibbs Measures and Decay of Correlations for Contact Anosov Flows
In this work we study strong spectral properties of Ruelle transfer operators related to a large family of Gibbs measures for contact
Anosov flows. The ultimate aim is to establish exponential decay of correlations for Hölder observables with respect to a very general
class of Gibbs measures. The approach invented in 1997 by Dolgopyat in “On decay of correlations in Anosov flows” and further developed
in Stoyanov (2011) is substantially refined here, allowing to deal with much more general situations than before, although we still
restrict ourselves to the uniformly hyperbolic case. A rather general procedure is established which produces the desired estimates
whenever the Gibbs measure admits a Pesin set with exponentially small tails, that is a Pesin set whose preimages along the flow have
measures decaying exponentially fast. We call such Gibbs measures regular. Recent results in Gouëzel and Stoyanov (2019) prove existence
of such Pesin sets for hyperbolic diffeomorphisms and flows for a large variety of Gibbs measures determined by Hölder continuous
potentials. The strong spectral estimates for Ruelle operators and well-established techniques lead to exponential decay of correlations
for Hölder continuous observables, as well as to some other consequences such as: (a) existence of a non-zero analytic continuation of
the Ruelle zeta function with a pole at the entropy in a vertical strip containing the entropy in its interior; (b) a Prime Orbit
Theorem with an exponentially small error.
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Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits
We study a class of measure-theoretic objects that we call
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Conspirituality : how new age conspiracy theories became a health threat
\"Conspirituality takes a deep dive into the troubling phenomenon of influencers who have curdled New Age spirituality and wellness with the politics of paranoia--peddling vaccine misinformation, tales of child trafficking, and wild conspiracy theories. In the early days of the COVID-19 pandemic, a disturbing social media trend emerged: a large number of yoga instructors and alt-health influencers were posting stories about a secretive global cabal bent on controlling the world's population with a genocidal vaccine. Instagram feeds that had been serving up green smoothie recipes and Mary Oliver poems became firehoses of Fox News links, memes from 4chan, and prophecies of global transformation. Since May 2020, Derek Beres, Matthew Remski and Julian Walker have used their Conspirituality podcast to expose countless facets of the intersection of alt-health practitioners with far-right conspiracy trolls. Now this expansive and revelatory book unpacks the follies, frauds, cons and cults that dominate the New Age and wellness spheres and betray the trust of people who seek genuine relief in this uncertain age. With analytical rigor and irreverent humor, Conspirituality offers an antidote to our times, helping readers recognize wellness grifts, engage with loved ones who've fallen under the influence, and counter lies and distortions with insight and empathy.\"--Publisher.
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Congruence Lattices of Ideals in Categories and (Partial) Semigroups
This monograph presents a unified framework for determining the congruences on a number of monoids and categories of transformations,
diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative process of stacking certain
normal subgroup lattices on top of each other to successively build congruence lattices of a chain of ideals. This is applied to several
specific categories of: transformations; order/orientation preserving/reversing transformations; partitions; planar/annular partitions;
Brauer, Temperley–Lieb and Jones partitions; linear and projective linear transformations; and partial braids. Special considerations
are needed for certain small ideals, and technically more intricate theoretical underpinnings for the linear and partial braid
categories.
eBook
Conformal Graph Directed Markov Systems on Carnot Groups
We develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped
with a sub-Riemannian metric. In particular, we develop the thermodynamic formalism and show that, under natural hypotheses, the limit
set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen’s parameter. We illustrate our results for a variety of examples
of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include
the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the
non-real classical rank one hyperbolic spaces.
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