Logic and geometric representations constitute an interdisciplinary framework that merges formal logical systems with spatial and diagrammatic structures. This field encompasses the study of classical ...

We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data ...

Geometric representation theory is a vibrant field that unites methods from algebraic geometry, category theory and homological algebra to probe the symmetries and invariants arising from algebraic ...

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University of Chicago mathematicians Alexander Beilinson and Vladimir Drinfeld have been awarded the prestigious Wolf Prize for Mathematics “for their groundbreaking work in algebraic geometry, ...

Within mathematics, there is a vast and ever expanding web of conjectures, theorems and ideas called the Langlands program. That program links seemingly disconnected subfields. It is such a force that ...

Cartography consists of the flat, simplified and conventional geometric representation of the earth's surface, presented in the form of maps, charts or blueprints. Because it is a two-dimensional ...

In the parable of the blind men and the elephant, several blind men each describe a different part of an elephant they are touching – a sharp tusk, a flexible trunk, or a broad leg – and disagree ...

We report the existence of an entorhinal cell type that fires when an animal is close to the borders of the proximal environment. The orientation-specific edge-apposing activity of these "border cells ...