This talk will focus on two aspects of vector bundles. One is the calculation and application of certain characteristic and secondary characteristic forms (i.e. Chern, Chern-Simons, and Bott-Chern forms). This part is joint work with Leon Takhtajan and Indranil Biswas. The second is to study certain fully nonlinear PDE akin to the Monge-AmpĂ©re equation arising from these differential geometric objects. An existence result or two will be presented along with the difficulties involved in the PDE. Moreover, other areas of geometry and physics from which the same PDE arise will be pointed out.

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Last updated: 01 Oct 2023