SEMINAR: Groups and Combinatorics Seminar: Foundations of hyperbolic geometry
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Groups and Combinatorics Seminar: Foundations of hyperbolic geometry |
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Abstract: The independent discovery by Lobachevsky and Bolyai of hyperbolic geometry in the 1830's was followed by slow acceptance of the subject from the 1860's on, with the publications of relevant parts of the correspondence of Gauss. A new phase was entered from 1903, when David Hilbert, in his work introducing the "calculus of ends", introduced an axiomatisation for hyperbolic plane geometry by adding a hyperbolic parallel axiom to the axioms for plane absolute geometry. In 1938, Karl Menger (of the famous Vienna Circle) made the important discovery that in hyperbolic geometry the concepts of betweenness and equidistance can be defined in terms of point-line incidence. Since an axiom system obtained by replacing all occurrences of betweenness and equidistance with their definitions in terms of incidence would look highly unnatural, Menger and his students looked for a more natural axiom system. This talk will be on joint work with Tim Penttila (Colorado State University) which highlights the stunning connections involving the Menger-like models of Cayley-Klein hyperbolic planes (over Euclidean fields), Moufang sets, Bachmann-Schmidt planes, and abstract ovals.
Contact |
Gabriel Verret
<[email protected]>
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Start |
Fri, 09 Oct 2015 15:00
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End |
Fri, 09 Oct 2015 16:00
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Submitted by |
Gabriel Verret <[email protected]>
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Last Updated |
Wed, 21 Oct 2015 10:39
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