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We use results of angular clustering measurements in 3000 sq. deg's of the FIRST radio survey to infer information on spatial clustering. Measurements are compared with CDM-model predictions. Clusteri...

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Ben-Sasson, Goldreich and Sudan showed that a binary error correcting code admitting a $2$-query tester cannot be good, i.e., it cannot have both linear distance and positive rate. The same holds when...

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We study sheaves on posets, showing that cosystolic expansion of such sheaves can be derived from local expansion conditions of the sheaf and the poset (typically a high dimensional expander). When th...

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Suppose $A$ is an Azumaya algebra over a ring $R$ and $σ$ is an involution of $A$ extending an order-$2$ automorphism $λ:R\to R$. We say $σ$ is extraordinary if there does not exist a Brauer-trivia...

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The Cheeger constant of a graph, or equivalently its coboundary expansion, quantifies the expansion of the graph. This notion assumes an implicit choice of a coefficient group, namely, $\mathbb{F}_2$....

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Let $k$ be a field and let $G$ be an affine algebraic group over $k$. Call a $G$-torsor weakly versal for a class of $k$-schemes $\cal C$ if it specializes to every $G$-torsor over a scheme in $\cal C...

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Formally verifying software properties is a highly desirable but labor-intensive task. Recent work has developed methods to automate formal verification using proof assistants, such as Coq and Isabell...

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Let $A$ be a finite dimensional algebra (possibly with some extra structure) over an infinite field $K$ and let $r\in\mathbb{N}$. The $r$-tuples $(a_1,\dots,a_r)\in A^r$ which fail to generate $A$ are...

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Let $R$ be a semilocal Dedekind domain with fraction field $F$. We show that two hereditary $R$-orders in central simple $F$-algebras which become isomorphic after tensoring with $F$ and with some fai...

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Generalizing a theorem of Albert, Saltman showed that an Azumaya algebra $A$ over a ring represents a $2$-torsion class in the Brauer group if and only if there is an algebra $A'$ in the Brauer class ...