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Mark A. Stern, Professor

Mark A. Stern

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.

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

Teaching (Spring 2019):

  • MATH 633.01, COMPLEX ANALYSIS Synopsis
    Physics 205, TuTh 08:30 AM-09:45 AM
Office Hours:

Monday and Tuesday 2-3
Education:

Ph.D.Princeton University1984
B.S.Texas A&M University1980
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)

  • 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   (More Publications)

  1. Lipnowski, M; Stern, M, Geometry of the Smallest 1-form Laplacian Eigenvalue on Hyperbolic Manifolds, Geometrical and Functional Analysis Gafa, vol. 28 no. 6 (December, 2018), pp. 1717-1755, Springer Nature [doi]  [abs]
  2. "Nonlinear Harmonic Forms and Indefinite Bochner Formulas " in Hodge Theory and L^2-Analysis, vol. 39 (2017), Higher Education Press
  3. 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]
  4. Stern, MA, Asymptotic Hodge Theory of Vector Bundles, Communications in Analysis and Geometry, vol. 23 no. 3 (December, 2015), pp. 559-609, International Press
  5. M.A. Stern, $C^{\infty}$ Stability, Canonical Maps, and Discrete Dynamics (Preprint, 2014) (arXiv:1410.8851.)
Recent Grant Support

  • Instanton Decay and Nonlinear Harmonic Forms, Simons Foundation, 3553857, 2015/09-2020/08.      
  • 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