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 2017):
 MATH 356.01, ELEM DIFFERENTIAL EQUAT
Synopsis
 Physics 259, TuTh 08:30 AM09:45 AM
 MATH 555.01, ORDINARY DIFF EQUATIONS
Synopsis
 Physics 047, TuTh 10:05 AM11:20 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  2014)
 Benoit Charbonneau (2007  2010)
 Bianca Santoro (2009)
 Anda Degeratu (December 17, 2002  2005)
 Recent Publications
(More Publications)
 Sergey A. Cherkis, Andres LarrainHubach, Mark Stern, Instantons on multiTaubNUT Spaces I: Asymptotic Form and Index Theorem,
arXiv:1608.00018
(Preprint, August, 2016) [abs]
 M.A. Stern and B. Charbonneau, Asymptotic Hodge Theory of Vector Bundles,
Comm. in Anal. and Geom., vol. 23 no. 3
(2015),
pp. 559609
 Charbonneau, B; Stern, M, Asymptotic Hodge Theory of Vector Bundles,
Geometry and Topology, vol. 23 no. 3
(2015),
pp. 559609 [DG/1111.0591], [0591] [abs]
 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.)
 Recent Grant Support
 Instanton Decay and Nonlinear Harmonic Forms, Simons Foundation, 3553857, 2015/092020/08.
 Bound states, singularities, and supersymmetry, NSF, 2002/07.
