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Countable state Markov shifts are a natural generalization of the well-known subshifts of finite type. They are the subject of current research both for their own sake and as models for smooth dynamic...
We show that strongly positively recurrent Markov shifts (including shifts of finite type) are classified up to Borel conjugacy by their entropy, period and their numbers of periodic points.
Let G denote a connected reductive group over a nonarchimedean local field F. Let K denote a special maximal parahoric subgroup of G(F). We establish a Satake isomorphism for the Hecke algebra...
We consider the problem of testing isomorphism of groups of order n given by Cayley tables. The trivial nlog n bound on the time complexity for the general case has not been improved over the past fou...
A normal Hall subgroup N of a group G is a normal subgroup with its order coprime with its index. Schur-Zassenhaus theorem states that every normal Hall subgroup has a complement subgroup, that is a s...
We study the complexity of testing if two given matroids are isomorphic. The problem is easily seen to be in p 2 . In the case of linear matroids, which are represented over polynomially growing fie...
Abstract: We give an elementary proof for Lewis Bowen's theorem saying that two Bernoulli actions of two free groups, each having arbitrary base probability spaces, are stably orbit equivalent. Our me...
Abstract: We investigate the Sherali-Adams lift & project hierarchy applied to a graph isomorphism polytope whose integer points encode the isomorphisms between two graphs. In particular, the Sherali-...
It is unknown whether two graphs can be tested for isomorphism in polynomial time. A classical approach to the Graph Isomorphism Problem is the d-dimensional Weisfeiler-Lehman algorithm.
A mapping between projections of C*-algebras preserving the orthogonality, is called an orthoisomorphism. We define the order-isomorphism mapping on C*-algebras, and using Dye's result, we prove in th...
We deduce a formula enumerating the isomorphism classes of extensions of a $\kp$-adic field $K$ with given ramification $e$ and inertia $f$. The formula follows from a simple group-theoretic lemma, pl...
Some of the 95 families of weighted K3 hypersurfaces have been known to have the isometric lattice polarizations. It is shown that weighted K3 hyper-surfaces in such families are to one-to-one corresp...
We study the complexity of testing if two given matroids are isomorphic. The problem is easily seen to be in Σp 2 . In the case of linear matroids, which are represented over polynomially growing fiel...
In this paper we show that the Fibered Isomorphism Conjecture of Farrell and Jones, corresponding to the stable topological pseudoisotopy functor, is true for the fundamental groups of a class of comp...

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