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Research Interests for Mark A. Stern

Research Interests: Geometric Analysis, Yang-Mills theory, Hodge theory, string theory

The focus of Professor Stern's research is the study of analytic problems arising in geometry, topology, and physics.

In recent work, Professor Stern has studied analytical, geometric, and topological questions arising from Yang-Mills theory, string theory, and Hodge 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 on vector bundles, (iv) the analysis of harmonic spinors on singular spin structures, and (v) non fredholm index theories and exotic fixed point theorems.

Recent Publications
  1. Cherkis, SA; Larrain-Hubach, A; Stern, M, Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem, Journal of Differential Geometry (December, 2019), International Press [abs]
  2. Cerbo, LFD; Stern, M, Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points, Communications in Analysis and Geometry (August, 2019), International Press [abs]
  3. Lipnowski, M; Stern, M, Geometry of the Smallest 1-form Laplacian Eigenvalue on Hyperbolic Manifolds, Geometrical and Functional Analysis Gafa, vol. 28 no. 6 (December, 2018), pp. 1717-1755, Springer Nature [doi[abs]
  4. Stern, M, "Nonlinear Harmonic Forms and Indefinite Bochner Formulas " in Hodge Theory and L^2-Analysis, vol. 39 (2017), Higher Education Press
  5. Stern, MA; Charbonneau, B, Asymptotic Hodge Theory of Vector Bundles, Communications in Analysis and Geometry, vol. 23 no. 3 (December, 2015), pp. 559-609, International Press
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320