# 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.

Pardon, W, and Stern, M. "Pure hodge structure on the L2-cohomology of varieties with isolated singularities." *Journal fur die Reine und Angewandte Mathematik* 533 (2001): 55-80.

Britto-Pacumio, R, Maloney, A, Strominger, A, and Stern, M. "Spinning bound states of two and three black holes." *Journal of High Energy Physics* 5.11 (2001): XLIV-19.

Sethi, S, and Stern, M. "The structure of the D0-D4 bound state." *Nuclear Physics B* 578.1-2 (2000): 163-198.

Sethi, S, and Stern, M. "Invariance theorems for supersymmetric Yang-Mills theories." *Advances in Theoretical and Mathematical Physics* 4.2 (2000): 1-12.

Stern, M, and Yi, P. "Counting Yang-Mills dyons with index theorems." *Physical Review D - Particles, Fields, Gravitation and Cosmology* 62.12 (2000): 1-15.

Sethi, S, and Stern, M. "Supersymmetry and the Yang-Mills effective action at finite N." *Journal of High Energy Physics* 3.6 (1999): XIV-16.

Paban, S, Sethi, S, and Stern, M. "Summing up instantons in three-dimensional Yang-Mills theories." *Advances in Theoretical and Mathematical Physics* 3.2 (1999): 1-18.

Paban, S, Sethi, S, and Stern, M. "Supersymmetry and higher derivative terms in the effective action of Yang-Mills theories." *Journal of High Energy Physics* 2.6 (1998): XXII-6.

Paban, S, Sethi, S, and Stern, M. "Constraints from extended supersymmetry in quantum mechanics." *Nuclear Physics B* 534.1-2 (1998): 137-154.

Sethi, S, and Stern, M. "D-brane bound states redux." *Communications in Mathematical Physics* 194.3 (1998): 675-705.