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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…
Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural class of infinite automata representing their observable computational behavior, called linearly bounded graphs.…
We study the a.s. convergence of a sequence of random embeddings of a fixed manifold into Euclidean spaces of increasing dimensions. We show that the limit is deterministic. As a consequence, we show that many intrinsic functionals of the…
We classify up to equivalence all finite-dimensional irreducible representations of PSL2(Z) whose restriction to the commutator subgroup is diagonalizable.
We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.
We construct a class of representations of the Heisenberg algebra in terms of the complex shift operators subject to the proper continuous limit imposed by the correspondence principle. We find a suitable Hilbert space formulation of our…
We study representations of the classical infinite dimensional real simple Lie groups $G$ induced from factor representations of minimal parabolic subgroups $P$. This makes strong use of the recently developed structure theory for those…
We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…
Let X be the mild solution to a semilinear stochastic partial differential equation. In this article, we develop methodology to sample from the infinite-dimensional diffusion bridge that arises from conditioning X on a linear transformation…
We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.
We show the equivalence between a probabilistic Turing machine and the time evolution of a one-dimensional Ising model, the Glauber model in one dimension, equilibrium positions representing the results of computations of the Turing…
We study the representation theory of the infinite type A Hecke algebra over a non-archimedean field in the case where the parameter is a pseudo-uniformizer. Specifically, we consider a family of representations, called almost-symmetric,…
A classification of (countable) direct limits of finite dimensional involution simple associative algebras over an algebraically closed field of arbitrary characteristic is obtained. This also classifies the corresponding dimension groups.…
We completely characterize perfect, permutative, irreducible representations of an ultragraph Leavitt path algebra. For this we extend to ultragraph Leavitt path algebras Chen's construction of irreducible representations of Leavitt path…
In the present work we study self-interacting diffusions following an infinite dimensional approach. First we prove existence and uniqueness of a solution with Markov property. Then we study the corresponding transition semigroup and, more…
In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.
It is shown that the question raised in Section 5.7 of [1] has an affirmative answer.
We perform the computations necessary to establish a multiplicity one statement for the irreducible representations of a finite spin group which in turn yields the classification of irreducible representations of finite spin groups. (The…
This paper deals with the representation theory of a locally finite quiver in which the number of paths between any two given vertices is finite. We first study some properties of the finitely presented or co-presented representations, and…
Kinematic algebras can be realised on geometric spaces and constrain the physical models that can live on these spaces. Different types of kinematic algebras exist and we consider the interplay of these algebras for non-relativistic limits…