# 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.

Lipnowski, M, and Stern, M. "Geometry of the smallest 1-form Laplacian eigenvalue on hyperbolic manifolds."

Stern, MA. "Mechanical D Branes and B Fields."

Stern, MA. "B fields from a Luddite perspective." Full Text

Cerbo, LFD, and Stern, M. "Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points." Open Access Copy