- Professor of Mathematics

**External address:**116 Physics Bldg, Durham, NC 27708

**Internal office address:**Box 90320, Durham, NC 27708-0320

**Phone:**(919) 660-2840

Skip to main content
# Mark A. Stern

**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

##### Geometry: Differential & Algebraic

##### Mathematical Physics

##### PDE & Dynamical Systems

##### Topology

##### Education & Training

## Pages

## Mathematics

## Academics

## Current Students

## Future Students

- Professor of Mathematics

geometric analysis, elliptic partial differential equations

geometric analysis, Yang Mills theory, Hodge theory, Index theory

Yang Mills theory, String theory

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, 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.

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.

Cherkis, SA, Larrain-Hubach, A, and Stern, M. "Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem."

120 Science Drive

117 Physics Building

Campus Box 90320

Durham, NC 27708-0320

phone: 919.660.2800

fax: 919.660.2821

dept@math.duke.edu