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Paul S. Aspinwall, Professor of Mathematics and Physics

Paul S. Aspinwall

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
Office Phone:  (919) 660-2874
Email Address: send me a message
Web Page:  http://www.cgtp.duke.edu/~psa

Teaching (Fall 2016):

  • MATH 371.01, COMBINATORICS Synopsis
    Physics 235, MW 01:25 PM-02:40 PM
Office Hours:

1:00 to 2:00pm each Tuesday
10:30am to 11:30am each Thursday

Education:

Theoretical Elementary Particle PhysicsOxford1991
Ph.D.University of Oxford (UK)1985
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

Curriculum Vitae
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)

  1. PS Aspinwall, Exoflops in two dimensions, Journal of High Energy Physics, vol. 2015 no. 7 (July, Preprint, 2015) [arXiv:1412.0612], [doi]
  2. PS Aspinwall and B Gaines, 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]
  3. PS Aspinwall, Some applications of commutative algebra to string theory, in Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday, scopus (2013), pp. 25-56, ISBN 9781461452928 [doi]  [abs]
  4. N Addington and PS Aspinwall, Categories of Massless D-Branes and del Pezzo Surfaces, arxiv, vol. 2013 no. 176 (May, 2013) [1305.5767v2], [doi]  [abs]
  5. P.S. Aspinwall and M.R. Plesser, Elusive Worldsheet Instantons in Heterotic String Compactifications, in Proceedings of Symposia in Pure Mathematics, vol. 85 (2012), pp. 33-52 [1106.2998]
Recent Grant Support

  • Moduli Spaces & String Theory, National Science Foundation, DMS-1207708, 2012/07-2017/06.      
  • Geometry and Mathematical Physics of D-Branes, National Science Foundation, DMS-0905923, 2009/09-2014/08.      
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  

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320