- Professor of Mathematics
Mark A. Stern
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.
Sethi, S, and Stern, M. "A comment on the spectrum of H-monopoles." Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 398.1-2 (1997): 47-51.
Sethi, S, Stern, M, and Zaslow, E. "Monopole and dyon bound states in N = 2 supersymmetric Yang-Mills theories." Nuclear Physics, Section B 457.3 (1995): 484-510. Full Text Open Access Copy
Stern, M. "Index theory for certain complete kähler manifolds." Journal of Differential Geometry 37.3 (January 1, 1993): 467-503.
Pardon, WL, and Stern, MA. "L2 -∂-cohomology of complex projective varieties." Journal of the American Mathematical Society 4.3 (January 1, 1991): 603-621. Full Text
Stern, M, and Saper, L. "L²-cohomology of arithmetic varieties." Annals of Mathematics 132.1 (1990): 1-69.
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.
Cherkis, SA, Larrain-Hubach, A, and Stern, M. "Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem."