Related papers: Generalized Schr\"odinger semigroups on infinite g…
Based on the main result presented in a recent paper, we derive Ambarzumian-type theorems for Schr\"odinger operators defined on quantum graphs. We recover existing results such as the classical theorem by Ambarzumian and establish some…
We consider the infinite family of Feynman graphs known as the "banana graphs" and compute explicitly the classes of the corresponding graph hypersurfaces in the Grothendieck ring of varieties as well as their Chern-Schwartz-MacPherson…
In this paper, we prove the infinite dimensionality of some local and global cohomology groups on abstract Cauchy-Riemann manifolds.
We present an extension of J. F. Colombeau's theory of nonlinear generalized functions to spaces of generalized sections of vector bundles. Our construction builds on classical functional analytic notions, which is the key to having a…
Semistability at infinity is an asymptotic property of finitely presented groups that is needed in order to effectively define the fundamental group at infinity for a 1-ended group. It is an open problem whether or not all finitely…
We use tools from free probability to study the spectra of Hermitian operators on infinite graphs. Special attention is devoted to universal covering trees of finite graphs. For operators on these graphs we derive a new variational formula…
We study the category $\mathcal{A}$ of smooth semilinear representations of the infinite symmetric group over the field of rational functions in infinitely many variables. We establish a number of results about the structure of…
We describe all finite subsemigroups of a free left regular band of infinite rank. Moreover, we show applications of this result in algebraic geometry and model theory.
We describe a special class of representations of an inverse semigroup S on Hilbert's space which we term "tight". These representations are supported on a subset of the spectrum of the idempotent semilattice of S, called the "tight…
Various semigroups of noninvertible supermatrices of the special (antitriangle) shape having nilpotent Berezinian which appear in supersymmetric theories are defined and investigated. A subset of them continuously represents left and right…
A first step towards a systematic theory of relative line bundles over SUSY-curves is presented. In this paper we deal with the case of relative line bundles over families of ordinary Riemann surfaces. Generalizations of the Gauss-Bonnet…
We construct small cancellation labellings for some infinite sequences of finite graphs of bounded degree. We use them to define infinite graphical small cancellation presentations of groups. This technique allows us to provide examples of…
Let $ H:=-\tfrac12\Delta+V$ be a one-dimensional continuum Schr\"odinger operator. Consider ${\hat H}:= H+\xi$, where $\xi$ is a translation invariant Gaussian noise. Under some assumptions on $\xi$, we prove that if $V$ is locally…
We show that one can define and effectively compute Stallings graphs for quasi-convex subgroups of automatic groups (\textit{e.g.} hyperbolic groups or right-angled Artin groups). These Stallings graphs are finite labeled graphs, which are…
We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…
In this paper we determine the generalized Weierstrass semigroup $ \widehat{H}(P_{\infty}, P_1, \ldots , P_{m})$, and consequently the Weierstrass semigroup $H(P_{\infty}, P_1, \ldots , P_{m})$, at $m+1$ points on the curves…
We prove a coarse version of Halin's Grid Theorem: Every one-ended, locally finite graph that contains the disjoint union of infinitely many rays as an asymptotic minor also contains the half-grid as an asymptotic minor. More generally, we…
In this paper, we define the notion of a virtually symmetric representation of representations of virtual braid groups and prove that many known representations are equivalent to virtually symmetric. Using one such representation, we define…
We study analytic properties of graph product of finite groups with a hyperbolic defining graph. This is done by studying dynamics on the Bowditch compactification of the extension graph, or the crossing graph, of graph product. In…
Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…