- Professor of Mathematics

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

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

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

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# 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

### Selected Grants

## Pages

## 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

Instanton Decay and Nonlinear Harmonic Forms awarded by Simons Foundation (Principal Investigator). 2015 to 2020

Chern awarded by National Science Foundation (Principal Investigator). 2010 to 2014

Positive Mass, Singularities, and Supersymmetry awarded by National Science Foundation (Principal Investigator). 2005 to 2010

Bound States, Singularities, and Supersymmetry awarded by National Science Foundation (Principal Investigator). 2002 to 2006

(98-0381) Non-Fredholm Index Theory, Matrix, Models, and Hodge Theory awarded by National Science Foundation (Principal Investigator). 1998 to 2003

(97-0445) Hodge Structures and L2 Cohomology awarded by National Science Foundation (Principal Investigator). 1995 to 1999

(96-0809) Hodge Structures and L2 Cohomology awarded by National Science Foundation (Principal Investigator). 1995 to 1999

(95-0287) Hodge Structures and L2 Cohomology awarded by National Science Foundation (Principal Investigator). 1995 to 1997

(94-0102) Presidential Young Investigator Award: Mathematical Sciences awarded by National Science Foundation (Principal Investigator). 1989 to 1994

(86-0081) Some New Spectral Invariants and Their Relationship to Automorphic Forms and Geodesics awarded by National Science Foundation (Principal Investigator). 1986 to 1988

""Nonlinear Harmonic Forms and Indefinite Bochner Formulas " in Hodge Theory and L^2-Analysis." Beijing: Higher Education Press, 2017. (Chapter)

Stern, MA. "Geometry of Stable Yang Mills Connections." *Advances in Geometric Analysis.* International Pressof Boston Incorporated, 2012.

Saper, L, and Stern, M. "Appendix to: On the shape of the contribution of a fixed point on the boundary. The case of Q-rank one, by M. Rapoport." *The zeta functions of Picard modular surfaces based on lectures delivered at a CRM Workshop in the spring of 1988.* Ed. R Langlands and D Ramakrishnan. Montréal: Centre De Recherches Mathématiques, 1992. 489-491. (Chapter)

Stern, MA. "Asymptotic Hodge Theory of Vector Bundles." *Communications in Analysis and Geometry* 23.3 (December 1, 2015): 559-609.

Degeratu, A, and Stern, M. "Witten Spinors on Nonspin Manifolds." *Communications in Mathematical Physics* 324.2 (2013): 301-350.
Full Text

Melnikov, I, Quigley, C, Sethi, S, and Stern, M. "Target spaces from chiral gauge theories." *Journal of High Energy Physics* 2013.2 (2013): 1-56.
Full Text

Quigley, C, Sethi, S, and Stern, M. "Novel Branches of (0,2) Theories." *JHEP* 1209.064 (2012). (Academic Article)

Quigley, C, Sethi, S, and Stern, M. "Novel branches of (0, 2) theories." *Journal of High Energy Physics* 2012.9 (2012).
Full Text

Stern, M. "Geometry of minimal energy Yang-Mills connections." *Journal of Differential Geometry* 86.1 (2010): 163-188.

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

Paban, S, Sethi, S, and Stern, M. "Non-commutativity and Supersymmetry." *Journal of High Energy Physics* 2002.03 (March 1, 2002): 012-012.
Full Text

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

Paban, S, Sethi, S, and Stern, M. "I. Non-commutativity and supersymmetry." *Journal of High Energy Physics* 6.3 (2002): 183-200.

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