Mark A. Stern

Mark A. Stern
  • Professor of Mathematics
External address: 116 Physics Bldg, Durham, NC 27708
Internal office address: Box 90320, Durham, NC 27708-0320
Phone: (919) 660-2840

Research Areas and Keywords

Analysis
geometric analysis, elliptic partial differential equations
Geometry: Differential & Algebraic
geometric analysis, Yang Mills theory, Hodge theory, Index theory
Mathematical Physics
Yang Mills theory, String theory
PDE & Dynamical Systems
geometric analysis, elliptic partial differential equations
Topology
Index theory

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.

Education & Training
  • Ph.D., Princeton University 1984

  • B.S., Texas A&M University 1980

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. "Lefschetz formulae for arithmetic varieties." Inventiones Mathematicae 115.1 (1994): 241-296. Full Text

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

SAPER, L, and STERN, M. "L2-COHOMOLOGY OF ARITHMETIC VARIETIES." ANNALS OF MATHEMATICS 132.1 (July 1990): 1-69. Full Text

Stern, M. "Eta invariants and Hermitian locally symmetric spaces." Journal of Differential Geometry 31.3 (1990): 771-789. Full Text

Stern, M. "L2-index theorems on locally symmetric spaces." Inventiones Mathematicae 96.2 (1989): 231-282. Full Text

Saper, L, and Stern, M. "L(2)-cohomology of arithmetic varieties." Proceedings of the National Academy of Sciences of the United States of America 84.16 (August 1987): 5516-5519. Full Text

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