Nonlinear Harmonic Forms and an Indefinite Bochner Formula
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We introduce the study of nonlinear harmonic forms. These are forms which minimize the $L_2$ energy in a cohomology class subject to a nonlinear constraint. In this note, we include only motivations and the most basic existence results. We also introduce a variant of the Bochner formula suitable for probing the structure of the intersection form of a 4-manifold.
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Professor of Mathematics
The focus of Professor Stern's research is the study of analytic problems arising in geometry, topology, physics, and number theory. In recent work, Professor Stern has studied analytical, geometric, and topological questions arising from Yang-Mills theory, Hodge theory, and number theory. These have led for example to a study of (i) stability questions arising in Yang Mills theory and harmonic maps, (ii) energy minimizing connections and instantons, (iii) new Hodge structures o