Mark A. Stern, Professor
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 YangMills 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:
Teaching (Fall 2018):
 MATH 635.01, FUNCTIONAL ANALYSIS
Synopsis
 Physics 227, WF 08:30 AM09:45 AM
 MATH 79090.04, MINICOURSE IN ADVANCED TOPICS
Synopsis
 Physics 205, MWF 10:20 AM11:10 AM
 Office Hours:
 Monday and Tuesday 23
 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)
 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)
 "Nonlinear Harmonic Forms and Indefinite Bochner Formulas " in
Hodge Theory and L^2Analysis, vol. 39
(2017), Higher Education Press
 Sergey A. Cherkis, Andres LarrainHubach, Mark Stern, Instantons on multiTaubNUT Spaces I: Asymptotic Form and Index Theorem,
arXiv:1608.00018
(Preprint, August, 2016) [abs]
 Stern, MA, Asymptotic Hodge Theory of Vector Bundles,
Communications in Analysis and Geometry, vol. 23 no. 3
(December, 2015),
pp. 559609, International Press
 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.
