# 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
Algebraic Geometry, Mirror Symmetry, Calabi-Yau Varieties, Derived Categories
##### Mathematical Physics
String Theory, Compactification, D-Brane Categories.

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.

##### Education & Training
• D.Phil., University of Oxford (UK) 1988

• B.A., University of Oxford (UK) 1985

Aspinwall, PS. "Point-like instantons and the Spin(32)/ℤ2 heterotic string." Nuclear Physics B 496.1-2 (1997): 149-176.

Aspinwall, PS, Morrison, DR, and Gross, M. "Stable singularities in string theory." Communications in Mathematical Physics 178.1 (1996): 115-134.

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 (1996): 81-88.

Aspinwall, PS. "Some relationships between dualities in string theory." Nuclear Physics B - Proceedings Supplements 46.1-3 (1996): 30-38. Full Text

Aspinwall, PS. "Enhanced gauge symmetries and Calabi-Yau threefolds." Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 371.3-4 (1996): 231-237.

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 (1996): 233-242.

Aspinwall, PS. "An N = 2 dual pair and a phase transition." Nuclear Physics B 460.1 (1996): 57-76. Full Text

Aspinwall, PS. "Enhanced gauge symmetries and K3 surfaces." Physics Letters B 357.3 (1995): 329-334. Full Text

Aspinwall, PS, and Greene, BR. "On the geometric interpretation of N = 2 superconformal theories." Nuclear Physics, Section B 437.1 (1995): 205-227. Full Text

Aspinwall, PS, and Morrison, DR. "U-duality and integral structures." Physics Letters B 355.1-2 (1995): 141-149. Full Text