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Paul Stephen Aspinwall

Professor of Mathematics
Box 90320, Durham, NC 27708-0320
244 Physics Bldg, Durham, NC 27708
Office hours 2:00 to 3:00pm each Friday
10:00 to 11:00am each Wednesday  


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.

Current Appointments & Affiliations

Professor of Mathematics · 2006 - Present Mathematics, Trinity College of Arts & Sciences
Associate Chair of the Department of Mathematics · 2016 - Present Mathematics, Trinity College of Arts & Sciences
Professor of Physics · 2006 - Present Physics, Trinity College of Arts & Sciences

Education, Training & Certifications

University of Oxford (United Kingdom) · 1988 D.Phil.
University of Oxford (United Kingdom) · 1985 B.A.