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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. "Nonlinear Harmonic Forms and Indefinite Bochner Formulas " in Hodge Theory and L^2-Analysis, vol. 39 (2017), HHigher Education Press
  2. Sergey A. Cherkis, Andres Larrain-Hubach, Mark Stern, Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem, arXiv:1608.00018 (Preprint, August, 2016) [abs]
  3. M.A. Stern and B. Charbonneau, Asymptotic Hodge Theory of Vector Bundles, Comm. in Anal. and Geom., vol. 23 no. 3 (2015), pp. 559-609
  4. Charbonneau, B; Stern, M, Asymptotic Hodge Theory of Vector Bundles, Geometry and Topology, vol. 23 no. 3 (2015), pp. 559-609 [DG/1111.0591], [0591[abs]
  5. M.A. Stern, $C^{\infty}$ Stability, Canonical Maps, and Discrete Dynamics (Preprint, 2014) (arXiv:1410.8851.)

 

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