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 Yang-Mills 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:

Office Location:	116 Physics Bldg, Durham, NC 27708
Office Phone:	(919) 660-2840
Email Address:
Web Page:	https://www.math.duke.edu/faculty/stern

Teaching (Fall 2019):

• MATH 555.01, ORDINARY DIFF EQUATIONS Synopsis

  Physics 205, TuTh 10:05 AM-11:20 AM

• MATH 790-90.03, MINICOURSE IN ADVANCED TOPICS Synopsis

  Physics 205, TuTh 01:25 PM-02:40 PM

Office Hours:

Monday and Tuesday 2-3

Education:

Ph.D.	Princeton University	1984
B.S.	Texas A&M University	1980

Specialties:

Geometry
Mathematical Physics

Research Interests: Geometric Analysis, Yang-Mills 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 Yang-Mills 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)

1. Lipnowski, M; Stern, M, Geometry of the Smallest 1-form Laplacian Eigenvalue on Hyperbolic Manifolds, Geometrical and Functional Analysis Gafa, vol. 28 no. 6 (December, 2018), pp. 1717-1755, Springer Nature [doi]  [abs]
2. Cerbo, LFD; Stern, M, Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points (April, 2017)  [abs]
3. Stern, M, "Nonlinear Harmonic Forms and Indefinite Bochner Formulas " in Hodge Theory and L^2-Analysis, vol. 39 (2017), Higher Education Press
4. Cherkis, SA; Larrain-Hubach, A; Stern, M, Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem (August, 2016)  [abs]
5. Stern, MA, Asymptotic Hodge Theory of Vector Bundles, Communications in Analysis and Geometry, vol. 23 no. 3 (December, 2015), pp. 559-609, International Press

Recent Grant Support

• Instanton Decay and Nonlinear Harmonic Forms, Simons Foundation, 3553857, 2015/09-2020/08.      
• Bound states, singularities, and supersymmetry, NSF, 2002/07.