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 bounds for eigenvalues of Laplace Beltrami operators, and (iv) new bounds for betti numbers.  Contact Info:
Teaching (Spring 2024):
 MATH 621.01, DIFFERENTIAL GEOMETRY
Synopsis
 Physics 227, WF 08:30 AM09:45 AM
 Office Hours:
 Wednesday: 1011, Thursday : 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)
 Postdocs Mentored
 Akos Nagy (2017  2020)
 Goncalo Oliveira (2014  2017)
 Luca Di Cerbo (2011  2014)
 Benoit Charbonneau (2007  2010)
 Bianca Santoro (2009)
 Anda Degeratu (December 17, 2002  2005)
 Recent Publications
(More Publications)
 Di Cerbo, LF; Stern, M, Price inequalities and Betti number growth on manifolds without conjugate points,
Communications in Analysis and Geometry, vol. 30 no. 2
(January, 2022),
pp. 297334, International Press [doi] [abs]
 Cherkis, SA; LarrainHubach, A; Stern, M, Instantons on multiTaubNUT Spaces I: Asymptotic Form and Index Theorem,
Journal of Differential Geometry, vol. 119 no. 1
(December, 2021),
pp. 172, International Press [abs]
 Cherkis, S; LarraĆnHubach, A; Stern, M, Instantons on multiTaubNUT Spaces II: Bow Construction,
Journal of Differential Geometry
(March, 2021), International Press [abs]
 Cerbo, LFD; Stern, M, On the Betti Numbers of Finite Volume Hyperbolic Manifolds
(September, 2020) [abs]
 Cerbo, LFD; Stern, M, Harmonic Forms, Price Inequalities, and BenjaminiSchramm Convergence
(September, 2019) [abs]
 Recent Grant Support
 The Geometry and Analysis of YangMills Instantons., Simons Foundation, 2023/092028/08.
 Instanton Decay and Nonlinear Harmonic Forms, Simons Foundation, 3553857, 2015/092022/08.
 Bound states, singularities, and supersymmetry, NSF, 2002/07.
