DAVID R. MORRISON

A.B. Princeton University

Ph.D. Harvard University

James B. Duke Professor

Areas of Expertise: Algebraic Geometry and Mathematical Physics

Research Summary:

Dr. Morrison studies complex algebraic geometry and related topics. His current primary research interests center around issues in algebraic geometry which have recently arisen in mathematical physics.

Physicists studying superstring theory (a promising approach to the construction of grand unified field theories) find that the ``strings'' of the theory must propagate in a 10-dimensional spacetime. Yet since we only observe four spacetime dimensions in the real world, the other six dimensions must be playing a different rôle. It turns out that the ``extra'' six dimensions form a type of complex algebraic variety called a Calabi-Yau threefold. These varieties had been studied by algebraic geometers (including Dr. Morrison) long before the connection with physics was discovered. Dr. Morrison has spent the last several years working in collaboration with physicists to further develop the physical theories based on these algebraic varieties. He has also devoted a substantial effort to finding mathematical explanations for some of the discoveries about these varieties made by physicists, particularly the one known as ``mirror symmetry.''

Recently, working in collaboration with Brian Greene and Andy Strominger, Dr. Morrison discovered a new phenomenon in certain superstring theories, in which charged black holes become massless and transform into elementary particles. This process dramatically alters the topology of the associated Calabi-Yau variety. One important consequence is that the thousands of known Calabi-Yau threefolds simply represent different aspects of a small number of physical theories, perhaps even a unique theory. Semi-popular accounts of this work appear in Science magazine (June 23, 1995), Science News (August 26, 1995), and Scientific American (January, 1996), among other places.

Recent Publications (Mathematics):

  1. Mirror symmetry and rational curves on quintic threefolds: A guide for mathematicians, J. Amer. Math. Soc. 6 (1993), 223-247.
  2. (with P. S. Aspinwall and B. R. Greene), The monomial-divisor mirror map, Internat. Math. Res. Notices (1993), 319-337.
  3. Compactifications of moduli spaces inspired by mirror symmetry, Journées de Géométrie Algébrique d'Orsay (Juillet 1992), Astérisque, vol. 218, Société Mathématique de France, 1993, pp. 243-271.
  4. Mirror symmetry and moduli spaces of superconformal field theories, Proc. Internat. Congr. Math. Zürich 1994 (S. D. Chatterji, ed.), vol. 2, Birkäuser Verlag, Basel, Boston, Berlin, 1995, pp. 1304-1314.
  5. Beyond the Kähler cone, Proc. of the Hirzebruch 65 Conference on Algebraic Geometry (M. Teicher, ed.), Israel Math. Conf. Proc., vol. 9, Bar-Ilan University, 1996, pp. 361-376.
  6. Making enumerative predictions by means of mirror symmetry, April 1995, 24 pp; Essays on Mirror Manifolds II, to appear.

Recent Publications (Physics):

  1. (with P. S. Aspinwall), Topological field theory and rational curves, Comm. Math. Phys. 151 (1993), 245-262.
  2. (with P. S. Aspinwall and B. R. Greene), Calabi-Yau moduli space, mirror manifolds and spacetime topology change in string theory, Nuclear Phys. B 416 (1994), 414-480.
  3. (with P. Candelas, X. de la Ossa, A. Font and S. Katz), Mirror symmetry for two parameter models (I), Nuclear Phys. B 416 (1994), 481-562.
  4. (with P. S. Aspinwall and B. R. Greene), Measuring small distances in N=2 sigma models, Nuclear Phys. B 420 (1994), 184-242.
  5. (with P. S. Aspinwall), Chiral rings do not suffice: N=(2,2) theories with nonzero fundamental group, Phys. Lett. B 334 (1994), 79-86.
  6. (with P. S. Aspinwall and B. R. Greene), Space-time topology change and stringy geometry, J. Math. Phys. 35 (1994), 5321-5337.
  7. (with P. Candelas, A. Font and S. Katz), Mirror symmetry for two parameter models - II, Nuclear Phys. B 429 (1994), 626-674.
  8. (with M. R. Plesser), Summing the instantons: Quantum cohomology and mirror symmetry in toric varieties, Nuclear Phys. B 440 (1995), 279-354.
  9. Where is the large radius limit?, Strings '93 (M. B. Halpern, G. Rivlis, and A. Sevrin, eds.), World Scientific, Singapore, 1995, pp. 311-315.
  10. (with P. S. Aspinwall), U-duality and integral structures, Phys. Lett. B 355 (1995), 141-149.
  11. (with B. R. Greene and A. Strominger), Black hole condensation and the unification of string vacua, Nuclear Phys. B 451 (1995), 109-120. (with B. R. Greene and M. R. Plesser), Mirror manifolds in higher dimension, Comm. Math. Phys. 173 (1995), 559-598.
  12. Mirror symmetry and the type II string, Trieste Conference on S-Duality and Mirror Symmetry, Nuclear Phys. B Proc. Suppl., vol. 46, 1996, pp. 146-155.
  13. (with M. R. Plesser), Towards mirror symmetry as duality for two-dimensional abelian gauge theories, Trieste Conference on S-Duality and Mirror Symmetry, Nuclear Phys. B Proc. Suppl., vol. 46, 1996, pp. 177-186.
  14. (with P. S. Aspinwall), Stable singularities in string theory, Comm. Math. Phys. 178 (1996), 115-134, (with an appendix by Mark Gross).
  15. (with C. Vafa), Compactifications of F-theory on Calabi-Yau threefolds - I, Nuclear Phys. B 473 (1996), 74-92.
  16. (with P. S. Aspinwall), String theory on K3 surfaces, April 1994, 14 pp; Essays on Mirror Manifolds II, to appear.
  17. (with S. Katz and M. R. Plesser), Enhanced gauge symmetry in type II string theory, January, 1996, 43 pp., Nuclear Phys. B, to appear.
  18. (with C. Vafa), Compactifications of F-theory on Calabi-Yau threefolds - II, March, 1996, 33 pp., Nuclear Phys. B, to appear.

Last modified September, 1996