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
Office Hours: 

Monday and Tuesday 2-3

Research Areas and Keywords

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
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

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

Stern, M. "L 2-index theorems on locally symmetric spaces." Inventiones Mathematicae 96.2 (June 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

Paban, S, Sethi, S, and Stern, M. "Non-commutativity and Supersymmetry(Published online)." Journal of High Energy Physics 2002.03: 012-012. Full Text