Related papers: Some results on random fields admitting a spectral…
We consider various counting questions for irreducible binomials over finite fields. We use various results from analytic number theory to investigate these questions.
Based on tiles and on the Coven-Meyerowitz property, we present some examples and some general constructions of spectral subsets of integers.
We present a construction of the Steinberg representation admitting an automatic pass to an infinite-dimensional limit.
The first part is expository: it explains how finite fields may be used to prove theorems on infinite fields by a reduction mod p process. The second part gives a variant of P.Smith's fixed point theorem which applies in any characteristic.
Spectrahedra are sets defined by linear matrix inequalities. Projections of spectrahedra are called semidefinitely representable sets. Both kinds of sets are of practical use in polynomial optimization, since they occur as feasible sets in…
We give a simplified complete proof for the classification of the selfinjective representation-finite algebras of finite dimension over an algebraically closed field. We explain the relations between the two different approaches and also to…
Gibbs random fields corresponding to systems of real-valued spins (e.g. systems of interacting anharmonic oscillators) indexed by the vertices of unbounded degree graphs with a certain summability property are constructed. It is proven that…
The category of admissible (in the appropriately modified sense of representation theory of totally disconnected groups) semi-linear representations of the automorphism group of an algebraically closed extension of infinite transcendence…
The irreducible decomposition of a unitary representation often contains continuous spectrum when restricted to a non-compact subgroup. The author singles out a nice class of branching problems where each irreducible summand occurs…
Using polynomial evaluation, we give some useful criteria to answer questions about divisibility of polynomials. This allows us to develop interesting results concerning the prime elements in the domain of coefficients. In particular, it is…
In an earlier paper, we determined the finite fields with indecomposable multiplicative groups and conjectured that there is no infinite field whose multiplicative group is indecomposable. In this paper, we prove this conjecture for several…
We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.
We previously showed that the inverse limit of standard-graded polynomial rings with perfect coefficient field is a polynomial ring, in an uncountable number of variables. In this paper, we show that the same result holds with arbitrary…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
We explore some properties of a recent representation of permanental vectors which expresses them as sums of independent vectors with components that are independent gamma random variables.
After a quick review of the representation theory of the symmetric group, we give an exposition of the tools brought about by the so-called half-infinite wedge representation of the infinite symmetric group. We show how these can be applied…
We review some recent results related to the self-assembly of infinite structures in the Tile Assembly Model. These results include impossibility results, as well as novel tile assembly systems in which shapes and patterns that represent…
We give an overview on recent results concerning additive unit representations. Furthermore the solutions of some open questions are included. The central problem is whether and how certain rings are (additively) generated by their units.…
Several structural properties of a universal algebra can be seen from the higher commutators of its congruences. Even on a finite algebra, the sequence of higher commutator operations is an infinite object. In the present paper, we exhibit…
Using the spectral theory of weakly convergent sequences of finite graphs, we prove the uniform existence of the integrated density of states for a large class of infinite graphs.