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 10dimensional 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 CalabiYau 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 CalabiYau variety. One important consequence is that
the thousands of known
CalabiYau threefolds simply represent different aspects of a small
number of physical theories, perhaps even a unique theory.
Semipopular 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):

Mirror symmetry and rational curves on quintic threefolds: A guide for
mathematicians, J. Amer. Math. Soc. 6 (1993), 223247.

(with P. S. Aspinwall and B. R. Greene), The monomialdivisor mirror
map, Internat. Math. Res. Notices (1993), 319337.

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. 243271.

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. 13041314.

Beyond the Kähler cone, Proc. of the Hirzebruch 65 Conference on
Algebraic Geometry (M. Teicher, ed.), Israel Math. Conf. Proc., vol. 9,
BarIlan University, 1996, pp. 361376.

Making enumerative predictions by means of mirror symmetry, April 1995,
24 pp; Essays on Mirror Manifolds II, to appear.
Recent Publications (Physics):

(with P. S. Aspinwall), Topological field theory and rational curves,
Comm. Math. Phys. 151 (1993), 245262.

(with P. S. Aspinwall and B. R. Greene), CalabiYau moduli space,
mirror manifolds and spacetime topology change in string theory, Nuclear
Phys. B 416 (1994), 414480.

(with P. Candelas, X. de la Ossa, A. Font and S. Katz), Mirror symmetry
for two parameter models (I), Nuclear Phys. B 416 (1994), 481562.

(with P. S. Aspinwall and B. R. Greene), Measuring small distances in
N=2 sigma models, Nuclear Phys. B 420 (1994), 184242.

(with P. S. Aspinwall), Chiral rings do not suffice: N=(2,2)
theories with nonzero fundamental group, Phys. Lett. B 334 (1994),
7986.

(with P. S. Aspinwall and B. R. Greene), Spacetime topology change and
stringy geometry, J. Math. Phys. 35 (1994), 53215337.

(with P. Candelas, A. Font and S. Katz), Mirror symmetry for two
parameter models  II, Nuclear Phys. B 429 (1994), 626674.

(with M. R. Plesser), Summing the instantons: Quantum cohomology and
mirror symmetry in toric varieties, Nuclear Phys. B 440 (1995),
279354.

Where is the large radius limit?, Strings '93 (M. B. Halpern, G. Rivlis,
and A. Sevrin, eds.), World Scientific, Singapore, 1995, pp. 311315.

(with P. S. Aspinwall), Uduality and integral structures, Phys. Lett.
B 355 (1995), 141149.

(with B. R. Greene and A. Strominger), Black hole condensation and the
unification of string vacua, Nuclear Phys. B 451 (1995), 109120.
(with B. R. Greene and M. R. Plesser), Mirror manifolds in higher
dimension, Comm. Math. Phys. 173 (1995), 559598.

Mirror symmetry and the type II string, Trieste Conference on SDuality
and Mirror Symmetry, Nuclear Phys. B Proc. Suppl., vol. 46, 1996,
pp. 146155.

(with M. R. Plesser), Towards mirror symmetry as duality for
twodimensional abelian gauge theories, Trieste Conference on SDuality and
Mirror Symmetry, Nuclear Phys. B Proc. Suppl., vol. 46, 1996,
pp. 177186.

(with P. S. Aspinwall), Stable singularities in string theory, Comm.
Math. Phys. 178 (1996), 115134, (with an appendix by Mark Gross).

(with C. Vafa), Compactifications of Ftheory on CalabiYau
threefolds  I, Nuclear Phys. B 473 (1996), 7492.

(with P. S. Aspinwall), String theory on K3 surfaces, April 1994, 14
pp; Essays on Mirror Manifolds II, to appear.

(with S. Katz and M. R. Plesser), Enhanced gauge symmetry in type II
string theory, January, 1996, 43 pp., Nuclear Phys. B, to appear.

(with C. Vafa), Compactifications of Ftheory on CalabiYau
threefolds  II, March, 1996, 33 pp., Nuclear Phys. B, to appear.
Last modified September, 1996