Mark A. Stern
- Professor of Mathematics
Research Areas and Keywords
Geometry: Differential & Algebraic
PDE & Dynamical Systems
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.
Stern, M. "Eta invariants and Hermitian locally symmetric spaces." Journal of Differential Geometry 31.3 (January 1, 1990): 771-789.
Saper, L, and Stern, M. "L₂-cohomology of arithmetic varieties." Proc Natl Acad Sci U.S.A. 84.16 (August 1987): 5516-5519.
Cerbo, LFD, and Stern, M. "Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points." Open Access Copy
Cherkis, SA, Larrain-Hubach, A, and Stern, M. "Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem."
Lipnowski, M, and Stern, M. "Geometry of the smallest 1-form Laplacian eigenvalue on hyperbolic manifolds."