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 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 Hodge structures on vector bundles, (iv) new bounds for eigenvalues of Laplace Beltrami operators, and (v) new bounds for betti numbers.
Office Hours
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 277080320
 stern@math.duke.edu (919) 6602840
 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
 (980381) NonFredholm Index Theory, Matrix, Models, and Hodge Theory awarded by National Science Foundation 1998  2003
 (970445) Hodge Structures and L2 Cohomology awarded by National Science Foundation 1995  1999
 (960809) Hodge Structures and L2 Cohomology awarded by National Science Foundation 1995  1999
 (950287) Hodge Structures and L2 Cohomology awarded by National Science Foundation 1995  1997
 (940102) Presidential Young Investigator Award: Mathematical Sciences awarded by National Science Foundation 1989  1994
 (860081) 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 1form Laplacian Eigenvalue on Hyperbolic Manifolds." Geometric and Functional Analysis 28, no. 6 (December 2018): 17171755. Full Text
 Cerbo, LFD, and Stern, M. "Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points." (April 18, 2017). Open Access Copy Link to Item
 Cherkis, SA, LarrainHubach, A, and Stern, M. "Instantons on multiTaubNUT Spaces I: Asymptotic Form and Index Theorem." (August 1, 2016). Link to Item
 Stern, MA. "Asymptotic Hodge Theory of Vector Bundles." Communications in Analysis and Geometry 23, no. 3 (December 1, 2015): 559609.
 Stern, M. "$C^{\infty}$ Stability, Canonical Maps, and Discrete Dynamics." (October 31, 2014). Link to Item
 Degeratu, A, and Stern, M. "Witten Spinors on Nonspin Manifolds." Communications in Mathematical Physics 324, no. 2 (December 2013): 301350. 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 (February 2013). Full Text
 "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." Journal of High Energy Physics 2012, no. 9 (September 2012). Full Text
 Stern, M. "Geometry of minimal energy YangMills connections." Journal of Differential Geometry 86, no. 1 (September 2010): 163188. Full Text
 "Fixed point theorems from a de Rham perspective." Asian Journal of Mathematics 13, no. 1 (October 26, 2009): 065088.
 STERN, MARK. "B FIELDS FROM A LUDDITE PERSPECTIVE." Quantum Theory and Symmetries (October 2004). Full Text
 "I. Noncommutativity and supersymmetry." Journal of High Energy Physics 6, no. 3 (March 1, 2002): 183200.
 Stern, MA. "Quantum Mechanical Mirror Symmetry, D Branes, and B fields." Eprint (2002). (Academic Article) Link to Item
 "Pure hodge structure on the L2cohomology of varieties with isolated singularities." Journal Fur Die Reine Und Angewandte Mathematik 533 (December 1, 2001): 5580.
 "Spinning bound states of two and three black holes." Journal of High Energy Physics 5, no. 11 (January 1, 2001): 119. Full Text
 "Counting YangMills dyons with index theorems." Physical Review D Particles, Fields, Gravitation and Cosmology 62, no. 12 (December 15, 2000): 115. Open Access Copy
 Sethi, S, and Stern, M. "The structure of the D0–D4 bound state." Nuclear Physics B 578, no. 12 (July 2000): 163198. Full Text
 "Invariance theorems for supersymmetric YangMills theories." Advances in Theoretical and Mathematical Physics 4, no. 2 (March 1, 2000): 112. Open Access Copy
 "Supersymmetry and the YangMills effective action at finite N." Journal of High Energy Physics 3, no. 6 (December 1, 1999).
 "Summing up instantons in threedimensional YangMills theories." Advances in Theoretical and Mathematical Physics 3, no. 2 (March 1, 1999): 118.
 "Supersymmetry and higher derivative terms in the effective action of YangMills 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. 12 (November 1998): 137154. Full Text
 Sethi, S, and Stern, M. "DBrane Bound States Redux." Communications in Mathematical Physics 194, no. 3 (June 1, 1998): 675705. Full Text
 Sethi, S, and Stern, M. "A comment on the spectrum of Hmonopoles." Physics Letters B 398, no. 12 (April 1997): 4751. Full Text
 Sethi, S, Stern, M, and Zaslow, E. "Monopole and dyon bound states in N = 2 supersymmetric YangMills theories." Nuclear Physics B 457, no. 3 (December 1995): 484510. Full Text Open Access Copy
 Stern, M. "Lefschetz formulae for arithmetic varieties." Inventiones Mathematicae 115, no. 1 (December 1994): 241296. Full Text
 Stern, M. "Index theory for certain complete Kähler manifolds." Journal of Differential Geometry 37, no. 3 (1993): 467503. Full Text
 Pardon, WL, and Stern, MA. "$L\sp 2\text–\overline\partial$cohomology of complex projective varieties." Journal of the American Mathematical Society 4, no. 3 (September 1, 1991): 603603. Full Text
 Saper, L, and Stern, M. "L 2 Cohomology of Arithmetic Varieties." The Annals of Mathematics 132, no. 1 (July 1990): 11. Full Text
 Stern, M. "Eta invariants and Hermitian locally symmetric spaces." Journal of Differential Geometry 31, no. 3 (1990): 771789. Full Text
 Stern, M. "L 2index theorems on locally symmetric spaces." Inventiones Mathematicae 96, no. 2 (June 1989): 231282. 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): 55165519. Full Text
 Paban, S, Sethi, S, and Stern, M. "Noncommutativity and Supersymmetry(Published online)." Journal of High Energy Physics 2002, no. 03: 012012. Full Text
 Stern, M. "Spectral asymmetry for manifolds of special holonomy." . Link to Item
 Stern, MA. "Mechanical D Branes and B Fields." . Link to Item

Book Sections
 Stern, M. ""Nonlinear Harmonic Forms and Indefinite Bochner Formulas " in Hodge Theory and L^2Analysis." . 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 Qrank 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 Langlands, R and Ramakrishnan, D, 489491. Montréal,: Centre De Recherches Mathématiques, 1992. (Chapter) Link to Item

 Teaching & Mentoring

Recent Courses
 Scholarly, Clinical, & Service Activities

Presentations & Appearances
 Monotonicity and Betti Number Bounds. Geometry Seminar. Harvard. October 23, 2018  October 23, 2018 2018
 Nahm Transform for ALF spaces. Geometry Seminar. SUNY Stonybrook. March 6, 2018 2018
 Monotonicity and Betti Number Bounds. Geometry Seminar. CUNY Graduate Seminar. February 15, 2018 2018
 Monotonicity and Betti number bounds. The Analysis of GaugeTheoretic 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 L2cohomology. 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 YangMills connections. October 20, 2009 2009
 Geometry of Minimal YangMills connections. April 6, 2009 2009
 Geometry of Stable YangMills connections. April 5, 2009 2009
 Minimal Energy YangMills Connections and Interpolating Instantons. October 28, 2008 2008

Outreach & Engaged Scholarship
 Judge . 2018 Yau Science Award. Tsinghua University. December 12, 2018  December 15, 2018 2018
 Judge. DogrunYau Science Award. Tsinghua University. December 2016  December 2016 2016
 Judge. 2015 Yau Math Award. Tsinghua University. December 2015  December 2015 2015
 Judge. 2014 Yau Math Award. Tsinghua University. December 2014  December 2014 2014
 Judge. Hang Lung Mathematics Award. City University Hong Kong. December 2014  December 2014 2014
 Judge. 2011 Yau Math Award. Tsinghua University. December 2011 2011
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