Mark A. Stern
- Professor of Mathematics
Monday and Tuesday 2-3
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, physics, and number theory.
In recent work, Professor Stern has studied analytical, geometric, and topological questions arising from Yang-Mills theory, Hodge theory, and number 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) new bounds for eigenvalues of Laplace Beltrami operators, and (v) new bounds for betti numbers.
Sethi, S, Stern, M, and Zaslow, E. "Monopole and dyon bound states in N = 2 supersymmetric Yang-Mills theories." Nuclear Physics B 457.3 (December 1995): 484-510. Full Text Open Access Copy
Stern, M. "Index theory for certain complete Kähler manifolds." Journal of Differential Geometry 37.3 (1993): 467-503. Full Text
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. "Eta invariants and Hermitian locally symmetric spaces." Journal of Differential Geometry 31.3 (1990): 771-789. Full Text