# Paul Stephen Aspinwall

## Professor of Mathematics

### Overview

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, and Fidkowski, LM. "Superpotentials for quiver gauge theories." *Journal of High Energy Physics* 2006.10 (2006).
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Aspinwall, PS. "D-branes on Calabi-Yau manifolds." (January 1, 2005): 1-152. (Chapter) Full Text

Aspinwall, PS, Horja, RP, and Karp, RL. "Massless D-branes on Calabi-Yau threefolds and monodromy." *Communications in Mathematical Physics* 259.1 (2005): 45-69.
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Aspinwall, PS, and Kallosh, R. "Fixing all moduli for M-theory on K3×K3." *Journal of High Energy Physics* 10 (2005): 1-20.
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Aspinwall, PS, and Melnikov, IV. "D-branes on vanishing del Pezzo surfaces." *Journal of High Energy Physics* 8.12 (2004): 901-930.

Aspinwall, PS. "The breakdown of topology at small scales." *Journal of High Energy Physics* 8.7 (2004): 453-463.

Aspinwall, PS, and Karp, RL. "Solitons in Seiberg-Witten theory and D-branes in the derived category." *Journal of High Energy Physics* 7.4 (2003): 1119-1137.

Aspinwall, PS. "A point's point of view of stringy geometry." *Journal of High Energy Physics* 7.1 (2003): 17-31.

Aspinwall, PS, and Douglas, MR. "D-brane stability and monodromy." *Journal of High Energy Physics* 6.5 (2002): 739-773.

Aspinwall, PS, and Lawrence, A. "Derived categories and zero-brane stability." *Journal of High Energy Physics* 5.8 (2001): XIV-26.