# 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

##### 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.

"Fixed point theorems from a de Rham perspective." *Asian Journal of Mathematics* 13.1 (October 26, 2009): 065-088.

STERN, MARK. "B FIELDS FROM A LUDDITE PERSPECTIVE." *Quantum Theory and Symmetries* (October 2004).
Full Text

"I. Non-commutativity and supersymmetry." *Journal of High Energy Physics* 6.3 (March 1, 2002): 183-200.

Stern, MA. "Quantum Mechanical Mirror Symmetry, D Branes, and B fields." *Eprint* (2002). (Academic Article)

"Pure hodge structure on the L2-cohomology of varieties with isolated singularities." *Journal Fur Die Reine Und Angewandte Mathematik* 533 (December 1, 2001): 55-80.

"Spinning bound states of two and three black holes." *Journal of High Energy Physics* 5.11 (January 1, 2001): 1-19.
Full Text

"Counting Yang-Mills dyons with index theorems." *Physical Review D Particles, Fields, Gravitation and Cosmology* 62.12 (December 15, 2000): 1-15.
Open Access Copy

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

"Invariance theorems for supersymmetric Yang-Mills theories." *Advances in Theoretical and Mathematical Physics* 4.2 (March 1, 2000): 1-12.
Open Access Copy

"Supersymmetry and the Yang-Mills effective action at finite N." *Journal of High Energy Physics* 3.6 (December 1, 1999).