# 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 Morrison, DR. "Point-like instantons on K3 orbifolds." *Nuclear Physics B* 503.3 (October 20, 1997): 533-564.
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Aspinwall, PS. "Point-like instantons and the Spin(32)/ℤ2 heterotic string." *Nuclear Physics B* 496.1-2 (July 7, 1997): 149-176.
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Aspinwall, PS, and Gross, M. "The SO(32) heterotic string on a K3 surface." *Physics Letters B* 387.4 (October 1996): 735-742.
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Aspinwall, PS, and Gross, M. "Heterotic-heterotic string duality and multiple K3 fibrations." *Physics Letters, Section B: Nuclear, Elementary Particle and High Energy Physics* 382.1-2 (August 1, 1996): 81-88.
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Aspinwall, PS, Morrison, DR, and Gross, M. "Stable singularities in string theory." *Communications in Mathematical Physics* 178.1 (May 1, 1996): 115-134.
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Aspinwall, PS, and Louis, J. "On the ubiquity of K3 fibrations in string duality." *Physics Letters, Section B: Nuclear, Elementary Particle and High Energy Physics* 369.3-4 (February 29, 1996): 233-242.
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Aspinwall, PS. "An N = 2 dual pair and a phase transition." *Nuclear Physics B* 460.1 (January 29, 1996): 57-76.
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Aspinwall, PS. "Some relationships between dualities in string theory." *Nuclear Physics B Proceedings Supplements* 46.1-3 (January 1, 1996): 30-38.
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Aspinwall, PS. "Enhanced gauge symmetries and K3 surfaces." *Physics Letters B* 357.3 (September 7, 1995): 329-334.
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Aspinwall, PS, and Greene, BR. "On the geometric interpretation of N = 2 superconformal theories." *Nuclear Physics, Section B* 437.1 (March 6, 1995): 205-227.
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