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math.DG2026
Line congruences associated to Appell's hypergeometric functions of rank-4
Matthew Ryan, Michael T. Schultz
Line congruences are the genesis of important examples of transformations of projective surfaces, such as the Laplace transform. We survey and review results related to this histor…
math.DG2025
Geometric aspects of rank-3 vector bundles over surfaces and 2-plane distributions on 5-manifolds
Brandon P. Ashley, Michael T. Schultz
We study geometric aspects of horizontal 2-plane distributions on the complement of the zero section in the 5-dimensional total space of a rank-3 vector bundle equipped with connec…
math.DG2019★ 1 cited
From the signature theorem to anomaly cancellation
Andreas Malmendier, Michael T. Schultz
We survey the Hirzebruch signature theorem as a special case of the Atiyah-Singer index theorem. The family version of the Atiyah-Singer index theorem in the form of the Riemann-Ro…