Proves a J-adapted Levi-Malcev decomposition for many 2-step solvable Lie algebras, confirming the Fino-Vezzoni conjecture for unimodular cases and characterizing SKT metrics on completely solvable ones.
Selfdual Solutions to Euclidean Gravity,
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Path integral quantization of topologically coupled massive p-form theories shows quantum duality breaking on non-trivial backgrounds, with the difference in required counterterms proportional to the Euler characteristic.
α' corrections leave the metric of self-dual instantons unmodified but correct the dilaton and axion fields via Gauss-Bonnet and Pontrjagin terms, with no net correction to the Euclidean action to first order.
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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A Levi-type decomposition on two-step solvable Lie algebras with a complex structure
Proves a J-adapted Levi-Malcev decomposition for many 2-step solvable Lie algebras, confirming the Fino-Vezzoni conjecture for unimodular cases and characterizing SKT metrics on completely solvable ones.
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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.