Paul S. Aspinwall, Professor of Mathematics and 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.  Contact Info:
Teaching (Spring 2017):
 MATH 431.01, ADVANCED CALCULUS I
Synopsis
 Physics 235, WF 08:30 AM09:45 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 CalabiYau Manifolds DBranes Duality
 Keywords:
Strings • CalabiYau • DBranes • 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 (1998/092001/09)
 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. 115, ISSN 03930440 [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. 2556, ISBN 9781461452928 [doi] [abs]
 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. 3352 [1106.2998]
 Recent Grant Support
 Moduli Spaces & String Theory, National Science Foundation, DMS1207708, 2012/072017/06.
 Geometry and Mathematical Physics of DBranes, National Science Foundation, DMS0905923, 2009/092014/08.
 Conferences Organized
