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 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.  Contact Info:
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
Teaching (Spring 2016):
 MATH 532.01, BASIC ANALYSIS II
Synopsis
 Physics 119, TuTh 08:30 AM09:45 AM
 Office Hours:
 Tuesday 3:004:00
Wednesday 3:004:00
 Education:
Ph.D.  Princeton University  1984 
B.S.  Texas A&M University  1980 
 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.)
 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. 156, ISSN 11266708 [1212], [doi] [abs]
 Anda Degeratu and M.A. Stern, Witten Spinors on Nonspin Manifolds,
Communications in Mathematical Physics, vol. 324 no. 2
(2013),
pp. 301350, ISSN 00103616 [DG/1112.0194], [0194], [doi] [abs]
 M.A. Stern, Geometry of stable YangMills 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, 2015/092020/08.
 Chern, National Science Foundation, 2010/092014/08.
 Asymptotic Hodge Theory and Instantons, National Science Foundation, DMS1005761, 2010/092013/08.
 Bound states, singularities, and supersymmetry, NSF, 2002/07.
