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 bounds for eigenvalues of Laplace Beltrami operators, and (iv) new bounds for betti numbers.

Contact Info:

Office Location:	116 Physics Bldg, Durham, NC 27708
Email Address:
Web Page:	https://www.math.duke.edu/faculty/stern

Teaching (Fall 2024):

• MATH 635.01, FUNCTIONAL ANALYSIS Synopsis

  Physics 119, TuTh 08:30 AM-09:45 AM

• MATH 790-90.03, MINICOURSE IN ADVANCED TOPICS Synopsis

  Physics 227, TuTh 01:25 PM-02:40 PM

• MATH 690-20.01, DIFFERENTIAL GEOMETRY (TOP) Synopsis

  Physics 227, WF 08:30 AM-09:45 AM

Office Hours:

Monday: 2-3,  Tuesday : 10-11

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)

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)

1. 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. 297-334, International Press [doi]  [abs]
2. Cherkis, SA; Larrain-Hubach, A; Stern, M, Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem, Journal of Differential Geometry, vol. 119 no. 1 (December, 2021), pp. 1-72, International Press  [abs]
3. Cherkis, S; Larraín-Hubach, A; Stern, M, Instantons on multi-Taub-NUT Spaces II: Bow Construction, Journal of Differential Geometry (March, 2021), International Press  [abs]
4. Cerbo, LFD; Stern, M, On the Betti Numbers of Finite Volume Hyperbolic Manifolds (September, 2020)  [abs]
5. Cerbo, LFD; Stern, M, Harmonic Forms, Price Inequalities, and Benjamini-Schramm Convergence (September, 2019)  [abs]

Recent Grant Support

• The Geometry and Analysis of Yang-Mills Instantons., Simons Foundation, 2023/09-2028/08.      
• Instanton Decay and Nonlinear Harmonic Forms, Simons Foundation, 3553857, 2015/09-2022/08.      
• Bound states, singularities, and supersymmetry, NSF, 2002/07.