## Mark A. Stern, Professor

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.

 Office Location: 116 Physics Bldg, Durham, NC 27708 Office Phone: (919) 660-2840 Email Address: Web Page: https://www.math.duke.edu/faculty/stern

Teaching (Spring 2018):

• MATH 653.01, ELLIPTIC PDE Synopsis
Physics 205, TuTh 08:30 AM-09:45 AM
• MATH 790-90.06, MINICOURSE IN ADVANCED TOPICS Synopsis
Physics 205, TuTh 10:05 AM-11:20 AM
Office Hours:

Tuesday 3:00-4:00
Wednesday 3:00-4:00
Education:

 Ph.D. Princeton University 1984 B.S. Texas A&M University 1980
Specialties:

Geometry
Mathematical Physics
Research Interests: Geometric Analysis, Yang-Mills theory, Hodge theory, string 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.

Current Ph.D. Students

• Jingxian Huang
• Phillip V. Andreae
Postdocs Mentored

• Luca Di Cerbo (2011 - 2014)
• Benoit Charbonneau (2007 - 2010)
• Bianca Santoro (2009)
• Anda Degeratu (December 17, 2002 - 2005)
Recent Publications

1. "Nonlinear Harmonic Forms and Indefinite Bochner Formulas " in Hodge Theory and L^2-Analysis, vol. 39 (2017), Higher Education Press
2. Sergey A. Cherkis, Andres Larrain-Hubach, Mark Stern, Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem, arXiv:1608.00018 (Preprint, August, 2016)  [abs]
3. Stern, MA, Asymptotic Hodge Theory of Vector Bundles, Communications in Analysis and Geometry, vol. 23 no. 3 (December, 2015), pp. 559-609, International Press
4. M.A. Stern, $C^{\infty}$ Stability, Canonical Maps, and Discrete Dynamics (Preprint, 2014) (arXiv:1410.8851.)
5. Mark Stern, Nonlinear Harmonic Forms and an Exotic Bochner Formula (Preprint, 2014) (arXiv:1411.0144.)
Recent Grant Support

• Instanton Decay and Nonlinear Harmonic Forms, Simons Foundation, 3553857, 2015/09-2020/08.
• Bound states, singularities, and supersymmetry, NSF, 2002/07.