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## 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.

Contact Info:
 Office Location: 116 Physics Bldg, Durham, NC 27708 Email Address: Web Page: https://www.math.duke.edu/faculty/stern

Teaching (Fall 2015):

• MATH 531.01, BASIC ANALYSIS I Synopsis
Physics 119, TuTh 08:30 AM-09:45 AM
• MATH 690-20.01, DIFFERENTIAL GEOMETRY (TOP) Synopsis
Physics 227, TuTh 11:45 AM-01:00 PM
Teaching (Spring 2016):

• MATH 532.01, BASIC ANALYSIS II Synopsis
Physics 119, TuTh 08:30 AM-09:45 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.

Curriculum Vitae
Current Ph.D. Students   (Former Students)

Postdocs Mentored

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

1. M.A. Stern, $C^{\infty}$ Stability, Canonical Maps, and Discrete Dynamics (Preprint, 2014) (arXiv:1410.8851.)
2. Mark Stern, Nonlinear Harmonic Forms and an Exotic Bochner Formula (Preprint, 2014) (arXiv:1411.0144.)
3. Ilarion V. Melnikov, Callum Quigley, Savdeep Sethi, M.A. Stern, Target spaces from chiral gauge theories, Journal of High Energy Physics, vol. 2013 no. 2 (December 12, 2012), pp. 1-56, ISSN 1126-6708 [1212], [doi]  [abs]
4. Anda Degeratu and M.A. Stern, Witten Spinors on Nonspin Manifolds, Communications in Mathematical Physics, vol. 324 no. 2 (2013), pp. 301-350, ISSN 0010-3616 [DG/1112.0194], [0194], [doi]  [abs]
5. M.A. Stern, Geometry of stable Yang--Mills connections, in Advanced Lectures in Mathematics Volume 21: Advances in Geometric Analysis (July, 2012), ISBN ISBN 9781571462480  [abs]
Recent Grant Support

• Instanton Decay and Nonlinear Harmonic Forms, Simons Foundation, 3553857, 2015/09-2020/08.
• Chern, National Science Foundation, 2010/09-2014/08.
• Asymptotic Hodge Theory and Instantons, National Science Foundation, DMS-1005761, 2010/09-2013/08.
• Bound states, singularities, and supersymmetry, NSF, 2002/07.

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320