Related papers: Independence and Alpern Multitowers

In \cite{Ch91a} it was shown that the billiard ball map for the periodic Lorentz gas has infinite topological entropy. In this article we study the set of points with infinite Lyapunov exponents. Using the cell structure developed in…

We prove that every perfectoid tower can be decomposed into a fiber product of perfectoid towers that are either $p$-torsion free or perfect of characteristic $p$. As an application, we show that separated perfectoid towers are reduced. We…

We generalize the concept of mutually unbiased bases (MUB) to measurements which are not necessarily described by rank one projectors. As such, these measurements can be a useful tool to study the long standing problem of the existence of…

The use of Bell's theorem in any application or experiment relies on the assumption of free choice or, more precisely, measurement independence, meaning that the measurements can be chosen freely. Here, we prove that even in the simplest…

We construct a complex entire function with arbitrary number of variables which has the following property: The infinite set consisting of all the values of all its partial derivatives of any orders at all algebraic points, including zero…

We show that for any positive integer $N$, there are only finitely many holomorphic eta quotients of level $N$, none of which is a product of two holomorphic eta quotients other than 1 and itself. This result is an analog of Zagier's…

We consider the algebras $M_p$ of Fourier multipliers and show that every bounded continuous function $f$ on $\mathbb R^d$ can be transformed by an appropriate homeomorphic change of variable into a function that belongs to $M_p(\mathbb…

For a positive measure set of nonuniformly expanding quadratic maps on the interval we effect a multifractal formalism, i.e., decompose the phase space into level sets of time averages of a given observable and consider the associated {\it…

A systematic review of the various topologies that can be defined on the projective Hilbert space P(H), i.e., on the set of the pure quantum states, is presented. It is shown that P(H) carries a natural topology as well as a natural…

We prove that there are groups in the constructible universe whose automorphism towers are highly malleable by forcing. This is a consequence of the fact that, under a suitable diamond hypothesis, there are sufficiently many highly rigid…

We classify invariant probability measures for non-elementary groups of automorphisms, on any compact K\"ahler surface X, under the assumption that the group contains a so-called "parabolic automorphism". We also prove that except in…

We establish new conditions that prevent the existence of (weak) normal integral bases in tame Galois extensions of number fields. This leads to the following result: under appropriate technical hypotheses, the existence of a normal…

Several variants of the Halpern-L\"auchli Theorem for trees of uncountable height are investigated. For $\kappa$ weakly compact, we prove that the various statements are all equivalent. We show that the strong tree version holds for one…

We formulate gauge theories based on Leibniz(-Loday) algebras and uncover their underlying mathematical structure. Various special cases have been developed in the context of gauged supergravity and exceptional field theory. These are based…

It is proved that there exists an (omega-1,omega-1) Souslin gap in the Boolean algebra (L(nu)/Fin,subseteq^*_ae) for every nonseparable measure nu. Thus a Souslin, also known as destructible, (omega-1,omega-1) gap in P(N)/Fin can always be…

The automorphism tower of a group is obtained by computing its automorphism group, the automorphism group of THAT group and so on, iterating transfinitely. Each group maps into the next using inner automorphisms and one takes a direct limit…

We prove that for every tower $\mathcal T$ there are $\aleph_1$-dense $A$ and $B$ so that any ``reasonable" forcing notion $\mathbb{P}$ -- an adjective that includes all known ones -- for making $A$ and $B$ isomorphic will add a…

In this paper we study the liftability property for piecewise continuous maps of compact metric spaces, which admit inducing schemes in the sense of Pesin and Senti [PS05, PS06]. We show that under some natural assumptions on the inducing…

We prove that for any two lattices $L, M \subseteq \mathbb{R}^d$ of the same volume there exists a measurable, bounded, common fundamental domain of them. In other words, there exists a bounded measurable set $E \subseteq \mathbb{R}^d$ such…

Two varieties $V, W$ of the same type are independent if there is a binary term $t(x,y)$ such that $V \models t(x,y) \approx x$ and $W \models t(x,y) \approx y$. In this note, we give necessary and sufficient conditions for two finite…