# Curriculum Vitae

## Mark A. Stern

 Box 90320, Durham, NC 27708-0320 (919) 660-2840 (office) (email)
Education

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

Geometric Analysis, Yang-Mills theory, Hodge theory, string theory

Professional Experience / Employment History

Duke University
Professor, Department of Mathematics, 1992 - present
Associate Professor, Department of Mathematics, 1988 - 1992
Assistant Professor, Department of Mathematics, 1985 - 1988
Member, Mathematics, 1988 - 1990
Member, Mathematics, 1984 - 1985
Awards, Honors, and Distinctions

Sloan Fellowship 1990-92
Presidential Young Investigator Award 1989-94
Fellow of the American Mathematical Society, American Mathematical Society, 0 2013
Sloan Research Fellowship-Mathematics, Alfred P. Sloan Foundation, 0 1990
Presidential Young Investigator, National Science Foundation, 0 1989

Major Grant Support

NSF

Recent Grant Support

• Instanton Decay and Nonlinear Harmonic Forms, Simons Foundation, 3553857, 2015/09-2021/08.
• Bound states, singularities, and supersymmetry, NSF, 2002/07.
Selected Recent Invited Talks

A Coarse Cheeger Inequality for one Forms, Duke, 18 March 2019
Monotonicity and Betti Number Bounds, Harvard, 23 October 2018
Nahm Transform for ALF spaces, SUNY Stonybrook, 6 March 2018
Monotonicity and Betti Number Bounds, CUNY Graduate Seminar, 15 February 2018
Monotonicity and Betti number bounds, BIRS, 29 August 2017
Spectral geometry of the 1 form Laplacian on hyperbolic manifolds., Hunter College, NYC, 6 May 2017
Instantons on ALF spaces, CUNY , 6 December 2016
Instantons on ALF spaces, University of Waterloo, 2 December 2016
Instantons on ALF spaces, Trieste, Italy, 24 October 2016
Instantons on ALF spaces, Harvard University, 11 October 2016
Decay and Moduli of Yang Mills Instantons, Newton Institute, July 21, 2015
Introduction to nonlinear harmonic forms, U. Maryland, March 30, 2015
Introduction to nonlinear harmonic forms, University of Houston, February 28, 2015
Introduction to nonlinear harmonic forms, Chinese University, Hong Kong, December 09, 2014
Introduction to nonlinear harmonic forms, Johns Hopkins, November 22, 2014
Instanton Decay, Texas A&M, April, 2014
Symmetry, singularity, and decay of Yang Mills fields, Texas A&M, March 20, 2014
Stability, Hodge theory, and Grassmann embeddings, Irvine, May 21, 2013
Hodge theory, Yang Mills, and Stability, U. of Arizona, Tucson, January 28, 2013
Asymptotic Hodge Theory of Vector Bundles, Sanya, Hainan, China, December 18, 2011
Stability, dynamics, and the quantum Hodge theory of vector bundles, Duke Mathematics, November 30, 2010
The Quantum Hodge Theory of Vector Bundles, CUNY Geometric Analysis 2010 Bubbling Phenomena and Non-Compactness, March 12, 2010
Geometry of Stable Yang-Mills connections, Graduate Center CUNY, October 20, 2009
Geometry of Minimal Yang-Mills connections, Warsaw, April 06, 2009
Geometry of Stable Yang-Mills connections, Texas A&M University, April 05, 2009
Minimal Energy Yang-Mills Connections and Interpolating Instantons, Mathematical Sciences Research Institute, October 28, 2008
Self-dual connections interpolating between components of the moduli space of flat connections on $T^3$, Montreal, CRM, August 27, 2007
Index Theory from a de Rham Perspective, South East Geometry Conference, Charleston, March 04, 2006
Positive mass conjecture for nonspin manifolds, Uniuversity of Chicago, May 2005
The positive mass conjecture for nonspin manifolds, Atlanta AMS meeting, January 2005
B fields from a Luddite perspective, QTS3 conference in Cincinnati, 11 September 2003
Doctoral Theses Directed

Janice McCarthy, L2 index theory and D-particle binding, (2009)
Jeffrey Streets, Ricci Yang-Mills Flow, (December 15, 2003 - 2007)
Editor IMRN 1991-1997

Publications

Papers Published

1. Cherkis, SA; Larrain-Hubach, A; Stern, M, Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem, Journal of Differential Geometry (December, 2019), International Press
2. Cerbo, LFD; Stern, M, Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points, Communications in Analysis and Geometry (August, 2019), International Press
3. 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
4. Stern, M, "Nonlinear Harmonic Forms and Indefinite Bochner Formulas " in Hodge Theory and L^2-Analysis, vol. 39 (2017), Higher Education Press
5. Stern, MA; Charbonneau, B, Asymptotic Hodge Theory of Vector Bundles, Communications in Analysis and Geometry, vol. 23 no. 3 (December, 2015), pp. 559-609, International Press
6. Stern, M, $C^{\infty}$ Stability, Canonical Maps, and Discrete Dynamics (October, 2014) (arXiv:1410.8851.)
7. Degeratu, A; Stern, M, Witten Spinors on Nonspin Manifolds, Communications in Mathematical Physics, vol. 324 no. 2 (2013), pp. 301-350, Springer Nature, ISSN 0010-3616
8. Melnikov, I; Quigley, C; Sethi, S; Stern, M, Target spaces from chiral gauge theories, Journal of High Energy Physics, vol. 2013 no. 2 (2013), pp. 1-56, Springer Nature, ISSN 1126-6708
9. Quigley, C; Sethi, S; Stern, M, Novel branches of (0, 2) theories, Journal of High Energy Physics, vol. 2012 no. 9 (September, 2012), Springer Science and Business Media LLC, ISSN 1029-8479
10. Quigley, C; Sethi, S; Stern, M, Novel branches of (0, 2) theories, Journal of High Energy Physics, vol. 2012 no. 9 (January, 2012)
11. Stern, MA, Geometry of Stable Yang Mills Connections, in Advances in Geometric Analysis (2012), International Pressof Boston Incorporated, ISBN 1571462481
12. Stern, M, Geometry of minimal energy Yang-Mills connections, Journal of Differential Geometry, vol. 86 no. 1 (2010), pp. 163-188, International Press of Boston, ISSN 0022-040X
13. Stern, M, Fixed point theorems from a de Rham perspective, Asian Journal of Mathematics, vol. 13 no. 1 (January, 2009), pp. 065-088, ISSN 1093-6106
14. STERN, M, B FIELDS FROM A LUDDITE PERSPECTIVE, in Proceedings of 3rd International Symposium on Quantum Theory and Symmetries (QTS3), Quantum Theory and Symmetries (October, 2004), World Scientific
15. Paban, S; Sethi, S; Stern, M, I. Non-commutativity and supersymmetry, Journal of High Energy Physics, vol. 6 no. 3 (March, 2002), pp. 183-200
16. Paban, S; Sethi, S; Stern, M, Non-commutativity and Supersymmetry, Journal of High Energy Physics, vol. 2002 no. 03 (March, 2002), pp. 012-012, Springer Science and Business Media LLC
17. Stern, MA, Quantum Mechanical Mirror Symmetry, D Branes, and B fields, Eprint (2002)
18. Britto-Pacumio, R; Maloney, A; Strominger, A; Stern, M, Spinning bound states of two and three black holes, Journal of High Energy Physics, vol. 5 no. 11 (January, 2001), pp. 1-19, ISSN 1029-8479
19. Pardon, W; Stern, M, Pure hodge structure on the L2-cohomology of varieties with isolated singularities, Journal Fur Die Reine Und Angewandte Mathematik, vol. 533 (2001), pp. 55-80
20. Stern, M; Yi, P, Counting Yang-Mills dyons with index theorems, Physical Review D, vol. 62 no. 12 (December, 2000), pp. 1-15, ISSN 0556-2821
21. Sethi, S; Stern, M, The structure of the D0-D4 bound state, Nuclear Physics B, vol. 578 no. 1-2 (July, 2000), pp. 163-198, Elsevier BV
22. Sethi, S; Stern, M, Invariance theorems for supersymmetric Yang-Mills theories, Advances in Theoretical and Mathematical Physics, vol. 4 no. 2 (January, 2000), pp. 1-12, ISSN 1095-0761
23. Paban, S; Sethi, S; Stern, M, Summing up instantons in three-dimensional Yang-Mills theories, Advances in Theoretical and Mathematical Physics, vol. 3 no. 2 (January, 1999), pp. 1-18, ISSN 1095-0761
24. Paban, S; Sethi, S; Stern, M, Constraints from extended supersymmetry in quantum mechanics, Nuclear Physics B, vol. 534 no. 1-2 (November, 1998), pp. 137-154, Elsevier BV
25. Sethi, S; Stern, M, D-brane bound states redux, Communications in Mathematical Physics, vol. 194 no. 3 (1998), pp. 675-705, Springer Nature
26. Sethi, S; Stern, M, A comment on the spectrum of H-monopoles, Physics Letters B, vol. 398 no. 1-2 (April, 1997), pp. 47-51, Elsevier BV
27. Sethi, S; Stern, M; Zaslow, E, Monopole and dyon bound states in N = 2 supersymmetric Yang-Mills theories, Nuclear Physics B, vol. 457 no. 3 (December, 1995), pp. 484-510, Elsevier BV, ISSN 0550-3213
28. Stern, M, Lefschetz formulae for arithmetic varieties, Inventiones Mathematicae, vol. 115 no. 1 (December, 1994), pp. 241-296, Springer Nature, ISSN 0020-9910
29. Stern, M, Index theory for certain complete kähler manifolds, Journal of Differential Geometry, vol. 37 no. 3 (January, 1993), pp. 467-503, International Press of Boston
30. Saper, L; 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 Langlands, R; Ramakrishnan, D (1992), pp. 489-491, Centre De Recherches Mathématiques
31. Pardon, WL; Stern, MA, L2 -∂-cohomology of complex projective varieties, Journal of the American Mathematical Society, vol. 4 no. 3 (January, 1991), pp. 603-621, American Mathematical Society (AMS)
32. SAPER, L; STERN, M, L2-COHOMOLOGY OF ARITHMETIC VARIETIES, Annals of Mathematics, vol. 132 no. 1 (July, 1990), pp. 1-69, JSTOR
33. Stern, M, Eta invariants and Hermitian locally symmetric spaces, Journal of Differential Geometry, vol. 31 no. 3 (January, 1990), pp. 771-789, International Press of Boston
34. Stern, M, L2-index theorems on locally symmetric spaces, Inventiones Mathematicae, vol. 96 no. 2 (June, 1989), pp. 231-282, Springer Nature, ISSN 0020-9910
35. Saper, L; Stern, M, L²-cohomology of arithmetic varieties, Proceedings of the National Academy of Sciences of the United States of America, vol. 84 no. 16 (August, 1987), pp. 5516-5519
36. Bill Pardon, Mark A Stern, Pure Hodge structures on the L2-cohomology of varieties with isolated singularities., J. Reine Angew. Math. 533 (2001) 55-80.
37. Sonia Paban, Savdeep Sethi, and Mark A. Stern, Summing Instantons in 3 dimensional Yang-Mills theories, Adv. Theor. Math. Phys, vol. 3, (1999).
38. S. Paban, S. Sethi, Mark A Stern, Supersymmetry and higher derivative terms in the effective action of Yang-Mills, J. High Energy Physics. 06:12 (1998)
39. Mark A. Stern, L^2-Cohomology and index theory of noncompact manifolds, Proceedings of Symposia in Pure Math. 54 (1993), 559-575
40. L. Saper, Mark A. Stern, Appendix to an article of Rapaport, Zeta functions of Picard Modular Varieties, R.P. Langlands and D. Ramakrishnan ed. CRM, Montreal (1992)
41. L. Saper and Mark A. Stern, L^2 cohomology of arithmetic varieties, Annals of Math. 132 (1990), 1-69
42. Mark A. Stern, L^2 index theorems on locally symmetric spaces, Inventiones 96 (1989), 231-282
43. L.Saper and Mark A. Stern, L^2 cohomology of arithmetic varieties, Proc. Natl. Acad. Sci. 84 (1987), 5516-5519
44. Mark A. Stern, L^2 index theorems on warped products, Thesis, Princeton University, 1984

Preprints

1. Mark Stern, Nonlinear Harmonic Forms and an Exotic Bochner Formula (2014) (arXiv:1411.0144.)
2. M.A. Stern, Spectral asymmetry for manifolds of special holonomy (2009)
3. M.A. Stern, Mechanical B fields and D branes (2003)