Paul Stephen Aspinwall
Professor of Mathematics
String theory is hoped to provide a theory of all fundamental physics encompassing both
quantum mechanics and general relativity. String theories naturally live in a large number of
dimensions and so to make contact with the real world it is necessary to ``compactify'' the
extra dimensions on some small compact space. Understanding the physics of the real
world then becomes a problem very closely tied to understanding the geometry of the space
on which one has compactified. In particular, when one restricts one's attention to
``supersymmetric'' physics the subject of algebraic geometry becomes particularly important.
Of current interest is the notion of ``duality''. Here one obtains the same physics by
compactifying two different string theories in two different ways. Now one may use our limited understanding of one
picture to fill in the gaps in our limited knowledge of the second picture. This appears to be an extremely powerful
method of understanding a great deal of string theory.
Both mathematics and physics appear to benefit greatly from duality. In mathematics one finds hitherto unexpected
connections between the geometry of different spaces. ``Mirror symmetry'' was an example of this but many more
remain to be explored. On the physics side one hopes to obtain a better understanding of nonperturbative aspects
of the way string theory describes the real world.
Aspinwall, PS. "Minimum distances in non-trivial string target spaces." Nuclear Physics B 431.1-2 (1994): 78-96.
Aspinwall, PS, and Morrison, DR. "Chiral rings do not suffice: N=(2,2) theories with nonzero fundamental group." Physics Letters B 334.1-2 (1994): 79-86. Full Text
Aspinwall, PS, Greene, BR, and Morrison, DR. "Measuring small distances in N = 2 sigma models." Nuclear Physics, Section B 420.1-2 (1994): 184-242. Full Text
Aspinwall, PS, Greene, BR, and Morrison, DR. "Calabi-Yau moduli space, mirror manifolds and spacetime topology change in string theory." Nuclear Physics B 416.2 (1994): 414-480.
Aspinwall, PS, Greene, BR, and Morrison, DR. "Space-time topology change and stringy geometry a." Journal of Mathematical Physics 35.10 (1994): 5321-5337.
Aspinwall, PS, Greene, BR, and Morrison, DR. "Multiple mirror manifolds and topology change in string theory." Physics Letters B 303.3-4 (1993): 249-259. Full Text
Aspinwall, PS, and Lütken, CA. "Quantum algebraic geometry of superstring compactifications." Nuclear Physics, Section B 355.2 (1991): 482-510. Full Text
Aspinwall, PS, and Lütken, CA. "Geometry of mirror manifolds." Nuclear Physics B 353.2 (1991): 427-461.