Related papers: Arcs, hypercubes, and graphs as quotients of proje…
We give a short review of a construction of Frink to obtain a metric space from a quasi-metric space. By an example we illustrate the limits of the construction.
We characterize the topological non-cancellative cones that are expressible as projective limits of finite powers of $[0,\infty]$. These are also the cones of lower semicontinuous extended-valued traces on AF C*-algebras. Our main result…
We work with quasianalytic classes of functions. Consider a real-valued function y = f(x) on an open subset U of Euclidean space, which satisfies a quasianalytic equation G(x, y) = 0. We prove that f is arc-quasianalytic (i.e., its…
These are the lecture notes for a course at the Summer School on "Applied Analysis" at the Technical University Chemnitz in September 2011. We start with the definition of a fractal algebra and show that the fractal property is enormously…
We prove several rigidity properties for random quotients of mapping class groups of surfaces, namely whose kernel is normally generated by the n-th steps of finitely many independent random walks. Firstly, we generalise a celebrated…
In this paper we provide a complete characterisation of transitive fractional jumps by showing that they can only arise from transitive projective automorphisms. Furthermore, we prove that such construction is feasible for arbitrarily large…
We obtain several sharp spectral bounds, approximations, and exact values for the isoperimetric number and related edge-expansion parameters of graphs. Our results focus on graph powers and on families of graphs with rich algebraic or…
We construct quantum metric structures on unital AF algebras with a faithful tracial state, and prove that for such metrics, AF algebras are limits of their defining inductive sequences of finite dimensional C*-algebras for the quantum…
We classify the gauge-invariant ideals in the C*-algebras of infinite directed graphs, and describe the quotients as graph algebras. We then use these results to identify the gauge-invariant primitive ideals in terms of the structural…
In this paper, we prove that any two birational projective varieties with finite quotient singularities can be realized as two geometric GIT quotients of a non-singular projective variety by a reductive algebraic group. Then, by applying…
We refine and advance the study of the local structure of idempotent finite algebras started in [A.Bulatov, The Graph of a Relational Structure and Constraint Satisfaction Problems, LICS, 2004]. We introduce a graph-like structure on an…
We introduce a new class of possibly infinite dimensional Lie algebras and study their structural properties. Examples of this new class of Lie algebras are finite dimensional simple Lie algebras containing a nonzero split torus, affine and…
Groups associated to surfaces isogenous to a higher product of curves can be characterised by a purely group-theoretic condition, which is the existence of a so-called ramification structure. In this paper, we prove that infinitely many…
We introduce the polygonalisation complex of a surface, a cube complex whose vertices correspond to polygonalisations. This is a geometric model for the mapping class group and it is motivated by works of Harer, Mosher and Penner. Using…
An arc is a set of vectors of the $k$-dimensional vector space over the finite field with $q$ elements ${\mathbb F}_q$, in which every subset of size $k$ is a basis of the space, i.e. every $k$-subset is a set of linearly independent…
We propose a notion of discrete elastic and area-constrained elastic curves in 2-dimensional space forms. Our definition extends the well-known discrete Euclidean curvature equation to space forms and reflects various geometric properties…
We give a survey of basic results on the cut norm and cut metric for graphons (and sometimes more general kernels), with emphasis on the equivalence problem. The main results are not new, but we add various technical complements, and a new…
Words are sequences of letters over a finite alphabet. We study two intimately related topics for this object: quasi-randomness and limit theory. With respect to the first topic we investigate the notion of uniform distribution of letters…
In this paper, the concept of quasi-finitely separating map and quasiapproximate identity are introduced. Based on these concepts, QFS-spaces and quasicontinuous maps are defined. Properties and characterizations of QFS-spaces are explored.…
In some varieties of algebras one can reduce the question of finding most general unifiers (mgus) to the problem of the existence of unifiers that fulfill the additional condition called projectivity. In this paper we study this problem for…