# 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

##### Geometry: Differential & Algebraic

##### Mathematical Physics

##### PDE & Dynamical Systems

##### Topology

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, 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.
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Stern, M. "Lefschetz formulae for arithmetic varieties." *Inventiones Mathematicae* 115.1 (1994): 241-296.
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Stern, M. "Index theory for certain complete Kähler manifolds." *Journal of Differential Geometry* 37.3 (1993): 467-503.
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Pardon, WL, and Stern, MA. "L2 -∂-cohomology of complex projective varieties." *Journal of the American Mathematical Society* 4.3 (January 1, 1991): 603-621.
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SAPER, L, and STERN, M. "L2-COHOMOLOGY OF ARITHMETIC VARIETIES." *ANNALS OF MATHEMATICS* 132.1 (July 1990): 1-69.
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Stern, M. "Eta invariants and Hermitian locally symmetric spaces." *Journal of Differential Geometry* 31.3 (1990): 771-789.
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Stern, M. "L2-index theorems on locally symmetric spaces." *Inventiones Mathematicae* 96.2 (1989): 231-282.
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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.
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