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### Paul S. Aspinwall, Professor of Mathematics; Associate Professor of 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.

Office Location: | 244 Physics Bldg, Durham, NC 27708 |

Office Phone: | (919) 660-2874 |

Email Address: | |

Web Page: | http://www.cgtp.duke.edu/~psa |

**Teaching (Fall 2018):**

- MATH 490.01,
*TOPICS IN MATHEMATICS*Synopsis- Physics 205, TuTh 10:05 AM-11:20 AM

**Office Hours:**- 1:00 to 2:00pm each Tuesday

10:30am to 11:30am each Thursday

**Education:**Theoretical Elementary Particle Physics Oxford 1991 D.Phil. University of Oxford (UK) 1988 B.A. University of Oxford (UK) 1985

**Specialties:**-
Mathematical Physics

Geometry

**Research Interests:***String Theory*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.

**Areas of Interest:**String Theory

Calabi-Yau Manifolds

D-Branes

Duality

**Keywords:**Strings • Calabi-Yau • D-Branes • Mirror

**Current Ph.D. Students**(Former Students)- Brian Fitzpatrick
- Kangkang Wang
- Benjamin Gaines

**Postdocs Mentored**- Nicolas Addington (August, 2012 - present)
- Stefano Guerra (September, 2007 - August, 2010)
- Robert Duivenvoorden (July, 2005 - August 30, 2006)
- K. Narayan (September 1, 2002 - August 30, 2004)
- Eric Sharpe (1998/09-2001/09)

**Recent Publications**(More Publications)- Aspinwall, PS; Plesser, MR,
*General mirror pairs for gauged linear sigma models*, The Journal of High Energy Physics, vol. 2015 no. 11 (November, 2015) [doi] - Aspinwall, PS,
*Exoflops in two dimensions*, The Journal of High Energy Physics, vol. 2015 no. 7 (July, Preprint, 2015) [arXiv:1412.0612], [doi] - Aspinwall, PS; Gaines, B,
*Rational curves and (0, 2)-deformations*, Journal of Geometry and Physics, vol. 88 (February, Accepted, 2015), pp. 1-15, ISSN 0393-0440 [arXiv:1404.7802], [doi] - Aspinwall, PS,
*Some applications of commutative algebra to string theory*, in Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday (2013), pp. 25-56, ISBN 9781461452928 [doi] [abs] - Addington, N; Aspinwall, PS,
*Categories of Massless D-Branes and del Pezzo Surfaces*, J. High Energy Phys. 7(176):39pp., 2013, vol. 2013 no. 176 (May, 2013) [1305.5767v2], [doi] [abs]

- Aspinwall, PS; Plesser, MR,