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) energy minimizing connections and instantons, (ii) non fredholm index theories and exotic fixed point theorems, and (iii) new Hodge structures on vector bundles (iv) the analysis of harmonic spinors on singular spin structures

Recent Publications
  1. B. Charbonneau and M. Stern, Asymptotic Hodge Theory of Vector Bundles, Geometry and Topology (Submitted, December 2, 2011) [DG/1111.0591], [0591] [abs]
  2. Anda Degeratu and M.A. Stern, Witten spinors on nonspin manifolds (Preprint, December 1, 2011) [DG/1112.0194], [0194] [abs]
  3. M.A. Stern, Geometry of minimal energy Yang-Mills connections, Journal of Differential Geometry, vol. 86 no. 1 (2010), pp. 163-188 [arXiv:0808.0667] [abs]
  4. M.A. Stern, Geometry of stable Yang--Mills connections, in "The Conference on Geometry" Proceedings (Submitted, 2010)
  5. M.A. Stern, Fixed point theorems from a de Rham perspective, Asian Journal of Mathematics (2009)