# Paul Stephen Aspinwall

- Professor 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, 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. "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.
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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.
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Aspinwall, PS, Morrison, DR, and Greene, BR. "The monomial-divisor mirror map." *International Mathematics Research Notices* 1993.12 (January 1, 1993): 319-337.
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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.
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Aspinwall, PS, and Morrison, DR. "Topological field theory and rational curves." *Communications in Mathematical Physics* 151.2 (1993): 245-262.
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Aspinwall, PS, and Lütken, CA. "Quantum algebraic geometry of superstring compactifications." *Nuclear Physics, Section B* 355.2 (1991): 482-510.
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Aspinwall, PS, and Lütken, CA. "Geometry of mirror manifolds." *Nuclear Physics B* 353.2 (1991): 427-461.