Related papers: Ergodic bounded constructions, Disjointness and We…

This is a work in progress, far from being in its final form whose purpose is to investigate thoroughly the structure of Berkovich analytic curves and its relation with the semi-stable reduction theorem (of which a new proof is given here,…

Assuming a particular case of Borisov--Alexeev--Borisov conjecture, we prove that finite subgroups of the automorphism group of a finitely generated field over Q have bounded orders. Further, we investigate which algebraic varieties have…

We prove that an analogue of Jordan's theorem on finite subgroups of general linear groups holds for the groups of biregular automorphisms of elliptic ruled surfaces. This gives a positive answer to a question of Vladimir L. Popov.

We discuss recurrence and ergodicity properties of random walks and associated skew products for large classes of locally compact groups and homogeneous spaces. In particular we show that a closed subgroup of a product of finitely many…

We generalise the main theorems from the paper "The Borel cardinality of Lascar strong types" by I. Kaplan, B. Miller and P. Simon to a wider class of bounded invariant equivalence relations. We apply them to describe relationships between…

We give a simple, short and self-contained presentation of Bourgain's discretised projection theorem from 2010, which is a fundamental tool in many recent breakthroughs in geometric measure theory, harmonic analysis, and homogeneous…

In this expository paper, we mainly study orthogonal arrays (OAs) of strength two having a row that is repeated $m$ times. It turns out that the Plackett-Burman bound (\cite{PB}) can be strengthened by a factor of $m$ for orthogonal arrays…

Rank one transformations serve as a source of examples in ergodic theory, showing variety of algebraic, asymptotic and spectral properties of dynamical systems. The properties of a rank one transformation are closely related to the weak…

We give an interpretation of the construction of torsors from preceding work (Bertram, Kinyon: Associative Geometries. I, J. Lie Theory 20) in terms of classical projective geometry. For the Desarguesian case, this leads to a reformulation…

We study the notions of weak rational ergodicity and rational weak mixing as defined by Jon Aaronson. We prove that various families of infinite measure-preserving rank-one transformations possess (or do not posses) these properties, and…

In this paper, we discuss several additional properties a power linear Keller map may have. The Structural Conjecture by Druzkowski in [Dru] asserts that two such properties are equivalent, but we show that one of this properties is…

Using Langer's construction of Bridgeland stability conditions on normal surfaces, we prove Reider-type theorems generalizing the work done by Arcara-Bertram in the smooth case. Our results still hold in positive characteristic or when…

In recent work, comonads and associated structures have been used to analyse a range of important notions in finite model theory, descriptive complexity and combinatorics. We extend this analysis to Hybrid logic, a widely-studied extension…

We prove a function-field analogue of Bourgain's $L^2$ pointwise ergodic theorem. Let $q$ be a power of a prime $p$, let $\mathbb{F}_q[t]$ be the ring of polynomials over the finite field $\mathbb{F}_q$, and let $\mathbb{F}_q[t][u]$ be the…

This work deals with the Landau equation in a bounded domain with the Maxwell reflection condition on the boundary for any (possibly smoothly position dependent) accommodation coefficient and for the full range of interaction potentials,…

There are many notions of rank in multilinear algebra: tensor rank, partition rank, slice rank, and strength (or Schmidt rank) are a few examples. Typically the rank $\le r$ locus is not Zariski closed, and understanding the closure (the…

In this series of two papers we will generalise the concept of extending a Lie algebroid by a Lie algebra bundle, leading to a notion of extending a Lie algebroid by another Lie algebroid whose orbits lie in the orbits of the former…

We establish a generalization of Bourgain double recurrence theorem and ergodic Bourgain-Sarnak's theorem by proving that for any aperiodic $1$-bounded multiplicative function $\boldsymbol{\nu}$, for any map $T$ acting on a probability…

We study regularity of bound states pertaining to embedded eigenvalues of a self-adjoint operator $H$, with respect to an auxiliary operator $A$ that is conjugate to $H$ in the sense of Mourre. We work within the framework of singular…

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.