Paul Stephen Aspinwall
Professor of Mathematics
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.
Moduli Spaces & String Theory awarded by National Science Foundation (Principal Investigator). 2012 to 2017
Geometry and Mathematical Physics of D-Branes awarded by National Science Foundation (Principal Investigator). 2009 to 2014
Algebraic Geometry and Quantum Field Theory of D-Branes awarded by National Science Foundation (Principal Investigator). 2006 to 2011
D-Brane Physics and Calabi-Yau Geometry awarded by National Science Foundation (Co-Principal Investigator). 2003 to 2007
Focused Research awarded by National Science Foundation (Co-Principal Investigator). 2000 to 2004
Aspinwall, PS. "Some applications of commutative algebra to string theory." Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday. November 1, 2013. 25-56. Full Text
Aspinwall, PS, and Plesser, MR. "General mirror pairs for gauged linear sigma models." Journal of High Energy Physics 2015.11 (November 2015). Full Text
Aspinwall, PS, and Plesser, MR. "Decompactifications and massless D-branes in hybrid models." Journal of High Energy Physics 2010.7 (2010). Full Text
Aspinwall, PS. "Topological D-branes and commutative algebra." Communications in Number Theory and Physics 3.3 (2009): 445-474.
Aspinwall, PS, Maloney, A, and Simons, A. "Black hole entropy, marginal stability and mirror symmetry." Journal of High Energy Physics 2007.7 (2007). Full Text
Aspinwall, PS. "Landau-Ginzburg to Calabi-Yau dictionary for D-branes." Journal of Mathematical Physics 48.8 (2007). Full Text