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Mark A Stern, Professor

Mark A Stern
Contact Info:
Office Location:  116 Physics
Office Phone:  (919) 660-2840
Email Address: send me a message
Web Page:  https://www.math.duke.edu/faculty/stern

Teaching (Spring 2015):

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

Wednesday 2:00-3:00
Thursday 2:00-3:00
Education:

B.S. Mathematics, Texas A & M, 1980 Ph.D. Mathematics, Princeton Univ, 1984
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. Anda Degeratu and M.A. Stern, Witten spinors on nonspin manifolds, Communications of Mathematical Physics 2013 (Accepted, October, 2013) [DG/1112.0194], [0194]  [abs]
  4. B. Charbonneau and M. Stern, Asymptotic Hodge Theory of Vector Bundles, Communications in Analysis and Geometry (Submitted, August, 2013) [DG/1111.0591], [0591]  [abs]
  5. Ilarion V. Melnikov, Callum Quigley, Savdeep Sethi, M.A. Stern, Target Spaces from Chiral Gauge Theories, JHEP vol. 1302 no. 111 (2013) (December 12, 2012) [1212]  [abs]
Recent Grant Support

  • 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