Introduces the three-cosystole invariant for matroids and proves its optimal upper bound among regular matroids of rank at most six via monotonicity under extensions and explicit estimates on maximal simple examples.
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The thesis derives an analytic family of Riemannian metrics on the Gromoll-Meyer exotic 7-sphere via Kaluza-Klein reduction, identifies the maximal-isometry case, and introduces a machine-learning algorithm for finding Einstein metrics on general manifolds.
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Higher cosystoles of matroids
Introduces the three-cosystole invariant for matroids and proves its optimal upper bound among regular matroids of rank at most six via monotonicity under extensions and explicit estimates on maximal simple examples.
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A Physicist's Visit to Exotic Spheres
The thesis derives an analytic family of Riemannian metrics on the Gromoll-Meyer exotic 7-sphere via Kaluza-Klein reduction, identifies the maximal-isometry case, and introduces a machine-learning algorithm for finding Einstein metrics on general manifolds.