Mark A. Stern
Professor of Mathematics
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.
Current Appointments & Affiliations
- Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 1992
Contact Information
- 116 Physics Bldg, Durham, NC 27708
- Box 90320, Durham, NC 27708-0320
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stern@math.duke.edu
(919) 660-2840
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https://www.math.duke.edu/faculty/stern
- Background
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Education, Training, & Certifications
- Ph.D., Princeton University 1984
- B.S., Texas A&M University 1980
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Duke Appointment History
- Chair, Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2006 - 2009
- Associate Chair, Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2003 - 2005
- Associate Professor with Tenure, Mathematics, Trinity College of Arts & Sciences 1989 - 1992
- Associate Professor, Mathematics, Trinity College of Arts & Sciences 1988 - 1989
- Assistant Professor, Mathematics, Trinity College of Arts & Sciences 1985 - 1988
- Recognition
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Awards & Honors
- Research
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Selected Grants
- Instanton Decay and Nonlinear Harmonic Forms awarded by Simons Foundation 2015 - 2020
- Chern awarded by National Science Foundation 2010 - 2014
- Positive Mass, Singularities, and Supersymmetry awarded by National Science Foundation 2005 - 2010
- Bound States, Singularities, and Supersymmetry awarded by National Science Foundation 2002 - 2006
- (98-0381) Non-Fredholm Index Theory, Matrix, Models, and Hodge Theory awarded by National Science Foundation 1998 - 2003
- (97-0445) Hodge Structures and L2 Cohomology awarded by National Science Foundation 1995 - 1999
- (96-0809) Hodge Structures and L2 Cohomology awarded by National Science Foundation 1995 - 1999
- (95-0287) Hodge Structures and L2 Cohomology awarded by National Science Foundation 1995 - 1997
- (94-0102) Presidential Young Investigator Award: Mathematical Sciences awarded by National Science Foundation 1989 - 1994
- (86-0081) Some New Spectral Invariants and Their Relationship to Automorphic Forms and Geodesics awarded by National Science Foundation 1986 - 1988
- Publications & Artistic Works
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Selected Publications
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Book Sections
- ""Nonlinear Harmonic Forms and Indefinite Bochner Formulas " in Hodge Theory and L^2-Analysis." Beijing: Higher Education Press, 2017. (Chapter)
- ""Nonlinear Harmonic Forms and Indefinite Bochner Formulas " in Hodge Theory and L^2-Analysis." Beijing: Higher Education Press, 2017. (Chapter)
- Stern, MA. "Geometry of Stable Yang Mills Connections." In Advances in Geometric Analysis. International Pressof Boston Incorporated, 2012.
- Saper, L, and Stern, M. "Appendix to: On the shape of the contribution of a fixed point on the boundary. The case of Q-rank one, by M. Rapoport." In The zeta functions of Picard modular surfaces based on lectures delivered at a CRM Workshop in the spring of 1988, edited by R Langlands and D Ramakrishnan, 489-491. Montréal: Centre De Recherches Mathématiques, 1992. (Chapter) Link to Item
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Journal Articles
- Stern, MA. "Asymptotic Hodge Theory of Vector Bundles." Communications in Analysis and Geometry 23, no. 3 (December 1, 2015): 559-609.
- Melnikov, I, Quigley, C, Sethi, S, and Stern, M. "Target spaces from chiral gauge theories." Journal of High Energy Physics 2013, no. 2 (February 2013). Full Text
- Degeratu, A, and Stern, M. "Witten Spinors on Nonspin Manifolds." Communications in Mathematical Physics 324, no. 2 (2013): 301-350. Full Text
- Quigley, C, Sethi, S, and Stern, M. "Novel branches of (0, 2) theories." Journal of High Energy Physics 2012, no. 9 (October 4, 2012). Full Text
- Quigley, C, Sethi, S, and Stern, M. "Novel Branches of (0,2) Theories." JHEP 1209, no. 064 (2012). (Academic Article) Link to Item
- Stern, M. "Geometry of minimal energy Yang-Mills connections." Journal of Differential Geometry 86, no. 1 (2010): 163-188.
- Stern, M. "Fixed point theorems from a de Rham perspective." Asian Journal of Mathematics 13, no. 1 (October 26, 2009): 065-088.
- Paban, S, Sethi, S, and Stern, M. "Non-commutativity and Supersymmetry." Journal of High Energy Physics 2002, no. 03 (March 1, 2002): 012-012. Full Text
- Paban, S, Sethi, S, and Stern, M. "I. Non-commutativity and supersymmetry." Journal of High Energy Physics 6, no. 3 (March 1, 2002): 183-200.
- Stern, MA. "Quantum Mechanical Mirror Symmetry, D Branes, and B fields." eprint (2002). (Academic Article) Link to Item
- Britto-Pacumio, R, Maloney, A, Strominger, A, and Stern, M. "Spinning bound states of two and three black holes." Journal of High Energy Physics 5, no. 11 (2001): XLIV-19.
- Pardon, W, and Stern, M. "Pure hodge structure on the L2-cohomology of varieties with isolated singularities." Journal fur die Reine und Angewandte Mathematik 533 (2001): 55-80.
- Sethi, S, and Stern, M. "The structure of the D0–D4 bound state." Nuclear Physics B 578, no. 1-2 (July 2000): 163-198. Full Text
- Sethi, S, and Stern, M. "Invariance theorems for supersymmetric Yang-Mills theories." Advances in Theoretical and Mathematical Physics 4, no. 2 (March 1, 2000): 1-12. Open Access Copy
- Stern, M, and Yi, P. "Counting Yang-Mills dyons with index theorems." Physical Review D - Particles, Fields, Gravitation and Cosmology 62, no. 12 (2000): 1-15. Open Access Copy
- Sethi, S, and Stern, M. "Supersymmetry and the Yang-Mills effective action at finite N." Journal of High Energy Physics 3, no. 6 (December 1, 1999).
- Paban, S, Sethi, S, and Stern, M. "Summing up instantons in three-dimensional Yang-Mills theories." Advances in Theoretical and Mathematical Physics 3, no. 2 (March 1, 1999): 1-18.
- Paban, S, Sethi, S, and Stern, M. "Supersymmetry and higher derivative terms in the effective action of Yang-Mills theories." Journal of High Energy Physics 2, no. 6 (December 1, 1998).
- Paban, S, Sethi, S, and Stern, M. "Constraints from extended supersymmetry in quantum mechanics." Nuclear Physics B 534, no. 1-2 (November 1998): 137-154. Full Text
- Sethi, S, and Stern, M. "D-Brane Bound States Redux." Communications in Mathematical Physics 194, no. 3 (June 1, 1998): 675-705. Full Text
- Sethi, S, and Stern, M. "A comment on the spectrum of H-monopoles." Physics Letters B 398, no. 1-2 (April 1997): 47-51. Full Text
- Sethi, S, Stern, M, and Zaslow, E. "Monopole and dyon bound states in N = 2 supersymmetric Yang-Mills theories." Nuclear Physics B 457, no. 3 (December 1995): 484-510. Full Text Open Access Copy
- Stern, M. "Lefschetz formulae for arithmetic varieties." Inventiones Mathematicae 115, no. 1 (1994): 241-296. Full Text
- Stern, M. "Index theory for certain complete Kähler manifolds." Journal of Differential Geometry 37, no. 3 (1993): 467-503. Full Text
- Pardon, WL, and Stern, MA. "L2 -∂-cohomology of complex projective varieties." Journal of the American Mathematical Society 4, no. 3 (January 1, 1991): 603-621. Full Text
- SAPER, L, and STERN, M. "L2-COHOMOLOGY OF ARITHMETIC VARIETIES." ANNALS OF MATHEMATICS 132, no. 1 (July 1990): 1-69. Full Text Link to Item
- Stern, M. "Eta invariants and Hermitian locally symmetric spaces." Journal of Differential Geometry 31, no. 3 (1990): 771-789. Full Text
- Stern, M. "L2-index theorems on locally symmetric spaces." Inventiones Mathematicae 96, no. 2 (1989): 231-282. Full Text
- Saper, L, and Stern, M. "L(2)-cohomology of arithmetic varieties." Proceedings of the National Academy of Sciences of the United States of America 84, no. 16 (August 1987): 5516-5519. Full Text
- Cerbo, LFD, and Stern, M. "Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points." Open Access Copy Link to Item
- Cherkis, SA, Larrain-Hubach, A, and Stern, M. "Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem." Link to Item
- Lipnowski, M, and Stern, M. "Geometry of the smallest 1-form Laplacian eigenvalue on hyperbolic manifolds." Link to Item
- Stern, M. "Spectral asymmetry for manifolds of special holonomy." Link to Item
- Stern, M. "$C^{\infty}$ Stability, Canonical Maps, and Discrete Dynamics." Link to Item
- Stern, MA. "Mechanical D Branes and B Fields." Link to Item
- Stern, MA. "B fields from a Luddite perspective." Full Text Link to Item
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- Teaching & Mentoring
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Recent Courses
- Scholarly, Clinical, & Service Activities
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Presentations & Appearances
- Monotonicity and Betti number bounds. The Analysis of Gauge-Theoretic Moduli Spaces. Banff International research Station. August 29, 2017 - August 29, 2017 2017
- Instantons on ALF Spaces. Gauge Theory and Special Geometry. Mathematical Congress of the Americas. July 25, 2017 - July 25, 2017 2017
- Spectral geometry of the 1 form Laplacian on hyperbolic manifolds.. Special Session on Geometry and Topology of Ball Quotients and Related Topics. AMS Eastern Sectional Meeting. May 6, 2017 - May 6, 2017 2017
- Instantons on ALF spaces. City University NY. CUNY . December 6, 2016 - December 6, 2016 2016
- Instantons on ALF spaces. Waterloo Geometry seminar. University of Waterloo. December 2, 2016 - December 2, 2016 2016
- In search of the second derivative. ICTP Elementary Notions Seminar. ICTP. October 28, 2016 - October 28, 2016 2016
- Instantons on ALF spaces. ICTP Geometry Seminar. ICTP. October 24, 2016 - October 24, 2016 2016
- Instantons on ALF spaces. Harvard Geometry Seminar. Harvard University. October 11, 2016 - October 11, 2016 2016
- Decay and Moduli of Yang Mills Instantons. Newton Institute. July 21, 2015 2015
- Introduction to nonlinear harmonic forms. U. Maryland. March 30, 2015 2015
- Introduction to nonlinear harmonic forms. Texas Geometry and Topology Conference. University of Houston. February 28, 2015 2015
- Introduction to nonlinear harmonic forms. Chinese University, Hong Kong. December 9, 2014 2014
- Introduction to nonlinear harmonic forms. Conference on Hodge Theory and L2-cohomology. Johns Hopkins. November 22, 2014 2014
- Instanton Decay. Conference on Heterotic Strings and (0,2) QFT. Texas A&M. April 2014 2014
- Symmetry, singularity, and decay of Yang Mills fields. Texas A&M. March 20, 2014 2014
- Stability, Hodge theory, and Grassmann embeddings. May 21, 2013 2013
- Hodge theory, Yang Mills, and Stability. January 28, 2013 2013
- Asymptotic Hodge Theory of Vector Bundles. December 18, 2011 2011
- Stability, dynamics, and the quantum Hodge theory of vector bundles. November 30, 2010 2010
- The Quantum Hodge Theory of Vector Bundles. March 12, 2010 2010
- Geometry of Stable Yang-Mills connections. October 20, 2009 2009
- Geometry of Minimal Yang-Mills connections. April 6, 2009 2009
- Geometry of Stable Yang-Mills connections. April 5, 2009 2009
- Minimal Energy Yang-Mills Connections and Interpolating Instantons. October 28, 2008 2008
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Outreach & Engaged Scholarship
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