Math @ Duke

Mark A Stern, Professor
 Contact Info:
Teaching (Spring 2015):
 MATH 532.01, BASIC ANALYSIS II
Synopsis
 Physics 119, TuTh 08:30 AM09:45 AM
Teaching (Fall 2015):
 MATH 531.01, BASIC ANALYSIS I
Synopsis
 Physics 119, TuTh 08:30 AM09:45 AM
 MATH 69020.01, DIFFERENTIAL GEOMETRY (TOP)
Synopsis
 Physics 227, TuTh 11:45 AM01:00 PM
 Office Hours:
 Wednesday 2:003:00
Thursday 2:003:00
 Education:
 B.S. Mathematics, Texas A & M, 1980
Ph.D. Mathematics, Princeton Univ, 1984
 Specialties:

Geometry
Mathematical Physics
 Research Interests: Geometric Analysis, YangMills 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 YangMills 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)
 M.A. Stern, $C^{\infty}$ Stability, Canonical Maps, and Discrete Dynamics
(Preprint, 2014) (arXiv:1410.8851.)
 Mark Stern, Nonlinear Harmonic Forms and an Exotic Bochner Formula
(Preprint, 2014) (arXiv:1411.0144.)
 Anda Degeratu and M.A. Stern, Witten spinors on nonspin manifolds,
Communications of Mathematical Physics 2013
(Accepted, October, 2013) [DG/1112.0194], [0194] [abs]
 B. Charbonneau and M. Stern, Asymptotic Hodge Theory of Vector Bundles,
Communications in Analysis and Geometry
(Submitted, August, 2013) [DG/1111.0591], [0591] [abs]
 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, DMS1005761, 2010/092013/08.
 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 277080320

