# Paul Stephen Aspinwall

- Professor of Mathematics
- Associate Chair of the Department of Mathematics
- Professor of Physics (Secondary)

**External address:**244 Physics Bldg, Durham, NC 27708

**Internal office address:**Box 90320, Durham, NC 27708-0320

**Phone:**(919) 660-2874

**Office Hours:**

1:00 to 2:00pm each Tuesday

10:30am to 11:30am each Thursday

### Research Areas and Keywords

##### Geometry: Differential & Algebraic

##### Mathematical Physics

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 Katz, S. "Computation of superpotentials for D-branes." *Communications in Mathematical Physics* 264.1 (2006): 227-253.
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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.

Aspinwall, PS. "Some navigation rules for D-brane monodromy." *Journal of Mathematical Physics* 42.12 (2001): 5534-5552.
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