Paul S. Aspinwall, Professor and Associate Chair

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.

Contact Info:

Office Location:	244 Physics Bldg, Durham, NC 27708
Email Address:
Web Page:	http://www.cgtp.duke.edu/~psa

Teaching (Spring 2025):

• MATH 219.08, MULTIVARIABLE CALCULUS Synopsis

  Physics 130, TuTh 08:30 AM-09:45 AM

• MATH 603.01, REPRESENTATION THEORY Synopsis

  Physics 119, TuTh 10:05 AM-11:20 AM

  (also cross-listed as PHYSICS 603.01)

Office Hours:

2:00 to 3:00pm each Friday
10:00 to 11:00am each Wednesday

Education:

D.Phil.	University of Oxford (United Kingdom)	1988
Theoretical Elementary Particle Physics	Oxford	1991
B.A.	University of Oxford (United Kingdom)	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

Curriculum Vitae

Current Ph.D. Students   (Former Students)

• Brian Fitzpatrick  
• Kangkang Wang  
• Benjamin Gaines  

Postdocs Mentored

• Nicolas Addington (August, 2012 - August, 2015)  
• 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)

1. Aspinwall, PS, String moduli spaces and parabolic factorizations, Journal of High Energy Physics, vol. 2025 no. 3 (March, 2025) [doi]  [abs]
2. Aspinwall, PS; Plesser, MR; Wang, K, Mirror Symmetry and Discriminants (February, 2017)  [abs]
3. Aspinwall, PS; Plesser, MR, General mirror pairs for gauged linear sigma models, Journal of High Energy Physics, vol. 2015 no. 11 (November, 2015), pp. 1-33, Springer Nature [doi]  [abs]
4. Aspinwall, PS, Exoflops in two dimensions, Journal of High Energy Physics, vol. 2015 no. 7 (July, 2015), Springer Nature [arXiv:1412.0612], [doi]  [abs]
5. Aspinwall, PS; Gaines, B, Rational curves and (0, 2)-deformations, Journal of Geometry and Physics, vol. 88 (February, 2015), pp. 1-15, Elsevier BV, ISSN 0393-0440 [arXiv:1404.7802], [doi]  [abs]

Conferences Organized

• Coorganizer : String Theory for Mathematicians 5/14/12 – 5/18/12. December 14, 2012, Coorganizer : String Theory for Mathematicians 5/14/12 – 5/18/12, December 2012  
• School on Mathematics in String and Field Theory, Director, June 2003