Related papers: Failure of Weak Approximation in Adjoint Groups
We consider here a recent conjecture stating that correlation functions and tail probabilities of finite time Lyapunov exponents would have the same power law decay in weakly chaotic systems. We demonstrate that this conjecture fails for a…
Post-Newtonian theory is considered a reliable effective expansion of General Relativity in the weak-field and slow-motion limit. We argue that such a belief is misplaced. In generic many-body relativistic dynamics, the absence of globally…
We prove that bounded conciseness is a closed property in the space of marked groups. As a consequence, we reformulate a conjecture of Fern\'andez-Alcober and Shumyatsky [7] about conciseness in the class of residually finite groups.
We explore the notion of approximate global symmetries in quantum field theory and quantum gravity. We show that a variety of conjectures about quantum gravity, including the weak gravity conjecture, the distance conjecture, and the…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
The Weak Gravity Conjecture imposes stringent constraints on effective field theories to allow for an ultraviolet completion within quantum gravity. While substantial evidence supports the conjecture across broad classes of string…
A special case of a conjecture raised by Forrest and Runde (Math. Zeit., 2005) asserts that the Fourier algebra of every non-abelian connected Lie group fails to be weakly amenable; this was aleady known to hold in the non-abelian compact…
We study groups endowed with Alexandroff topologies and show that no non-discrete Alexandroff topology can turn a group into a topological group. This settles negatively the basic existence problem for Alexandroff topological groups.…
Positive $C_0$-semigroups that occur in concrete applications are, more often than not, irreducible. Therefore a deep and extensive theory of irreducibility has been developed that includes characterizations, perturbation analysis, and…
Consider a finite l-group acting on the affine space of dimension n over a field k, whose characteristic differs from l. We prove the existence of a fixed point, rational over k, in the following cases: --- The field k is p-special for some…
We prove that a finite group is rational if and only if it has a set of permutation characters which separate conjugacy classes. It follows from this that a finite group is rational if and only if it has a representation as a permutation…
We introduce the notions of $\varepsilon$-approximate fixed point and weak $\varepsilon$-approximate fixed point. We show that for a group of unitary matrices even the existence of a nontrivial weak $\varepsilon$-approximate fixed point for…
Rational approximations are introduced and studied in granular graded rough sets and generalizations thereof by the first author in recent research papers. The concept of rationality is determined by related ontologies and coherence between…
We classify all pairs (G,V) with G a closed subgroup in a classical group with natural module V over the complex numbers such that G has the same composition factors on the kth tensor power of V, for a fixed (small) k. In particular, we…
In this article, we prove a strong relative Novikov conjecture for any pair of groups that are coarsely embeddable into Hilbert space.
This is an expostion of various aspects of amenability and paradoxical decompositions for groups, group actions and metric spaces. First, we review the formalism of pseudogroups, which is well adapted to stating the alternative of Tarski,…
This is an expository article, based on a lecture course given at CRM Barcelona in December 2009. The purpose of these notes is to prove, in a reasonably self-contained way, that finiteness of the Tate-Shafarevich group implies the parity…
In this article we formulate a version of the analytic Novikov conjecture for semigroups rather than groups, and show that the descent argument from coarse geometry generalises effectively to this new situation.
We give the first examples of rationally inessential but macroscopically large manifolds. Our manifolds are counterexamples to the Dranishnikov rationality conjecture. For some of them we prove that they do not admit a metric of positive…
A group of individuals wishes to classify $m$ objects into $n$ categories in such a way that no class is left empty, a condition known as surjectivity. The opinions of the individuals are aggregated separately for each object using an…