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, 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.

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 (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.

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

Saper, L, and Stern, M. "L²-cohomology of arithmetic varieties." Proc Natl Acad Sci U.S.A. 84.16 (August 1987): 5516-5519.

Pages