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. "Landau-Ginzburg to Calabi-Yau dictionary for D-branes." Journal of Mathematical Physics 48.8 (September 7, 2007). Full Text
Aspinwall, PS, Maloney, A, and Simons, A. "Black hole entropy, marginal stability and mirror symmetry." Journal of High Energy Physics 2007.7 (July 1, 2007). Full Text
Aspinwall, PS, Horja, RP, and Karp, RL. "Massless D-branes on Calabi-Yau threefolds and monodromy." Communications in Mathematical Physics 259.1 (October 1, 2005): 45-69. Full Text
Aspinwall, PS, and Melnikov, IV. "D-branes on vanishing del Pezzo surfaces." Journal of High Energy Physics 8.12 (December 1, 2004): 901-930.
Aspinwall, PS. "The breakdown of topology at small scales." Journal of High Energy Physics 8.7 (July 1, 2004): 453-463.