Mark A. Stern | Scholars@Duke

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.

Office Hours

Monday and Tuesday 2-3

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
stern@math.duke.edu (919) 660-2840
https://www.math.duke.edu/faculty/stern

Background
Education, Training, & Certifications
- Ph.D., Princeton University 1984
- B.S., Texas A&M University 1980
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
Awards & Honors
Research
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
Selected Publications
- Academic Articles
  - Lipnowski, M, and Stern, M. "Geometry of the Smallest 1-form Laplacian Eigenvalue on Hyperbolic Manifolds." Geometric and Functional Analysis 28, no. 6 (December 2018): 1717-1755. Full Text
  - Stern, MA. "Asymptotic Hodge Theory of Vector Bundles." Communications in Analysis and Geometry 23, no. 3 (December 1, 2015): 559-609.
  - Degeratu, A, and Stern, M. "Witten Spinors on Nonspin Manifolds." Communications in Mathematical Physics 324, no. 2 (2013): 301-350. Full Text
  - Melnikov, I, Quigley, C, Sethi, S, and Stern, M. "Target spaces from chiral gauge theories." Journal of High Energy Physics 2013, no. 2 (2013): 1-56. 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.
  - STERN, MARK. "B FIELDS FROM A LUDDITE PERSPECTIVE." Quantum Theory and Symmetries (October 2004). Full Text
  - 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
  - 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 (December 1, 2001): 55-80.
  - 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 (January 1, 2001): 1-19. Full Text
  - 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
  - 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
- 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
Teaching & Mentoring
Recent Courses
- MATH 635: Functional Analysis 2018
- MATH 653: Elliptic Partial Differential Equations 2018
- MATH 790-90: Minicourse in Advanced Topics 2018
- MATH 356: Elementary Differential Equations 2017
- MATH 555: Ordinary Differential Equations 2017
- MATH 532: Basic Analysis II 2016
- MATH 799: Special Readings 2016
Scholarly, Clinical, & Service Activities
Presentations & Appearances
Outreach & Engaged Scholarship
- Outreach Activities. December 2011 2011
- Outreach Activities. December 2011 2011

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Education, Training, & Certifications

Duke Appointment History

Awards & Honors

Selected Grants

Selected Publications

Academic Articles

Book Sections

Recent Courses

Presentations & Appearances

Outreach & Engaged Scholarship