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.
Office Hours
10:30am to 11:30am each Thursday
Current Appointments & Affiliations
 Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2006
 Professor of Physics, Physics, Trinity College of Arts & Sciences 2006
Contact Information
 244 Physics Bldg, Durham, NC 27708
 psa@cgtp.duke.edu (919) 6602874
 http://www.cgtp.duke.edu/~psa
 Background

Education, Training, & Certifications
 D.Phil., University of Oxford (UK) 1988
 B.A., University of Oxford (UK) 1985

Duke Appointment History
 Associate Chair of Mathematics, Mathematics, Trinity College of Arts & Sciences 2010  2017
 Interim Chair of the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2015
 Associate Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2000  2006
 Associate Professor of Physics, Physics, Trinity College of Arts & Sciences 2001  2006
 Assistant Professor of Physics, Physics, Trinity College of Arts & Sciences 1997  2001
 Assistant Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 1997  2000
 Recognition

Awards & Honors
 Research

Selected Grants
 Moduli Spaces & String Theory awarded by National Science Foundation 2012  2017
 Geometry and Mathematical Physics of DBranes awarded by National Science Foundation 2009  2014
 Algebraic Geometry and Quantum Field Theory of DBranes awarded by National Science Foundation 2006  2011
 DBrane Physics and CalabiYau Geometry awarded by National Science Foundation 2003  2007
 Focused Research awarded by National Science Foundation 2000  2004
 Publications & Artistic Works

Selected Publications

Book Sections
 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, 2556. November 1, 2013. Full Text

Journal Articles
 Aspinwall, PS, and Plesser, MR. "General mirror pairs for gauged linear sigma models." Journal of High Energy Physics 2015, no. 11 (November 2015). Full Text
 Aspinwall, PS. "Exoflops in two dimensions." Journal of High Energy Physics 2015, no. 7 (July 2015). Full Text
 Aspinwall, PS, and Gaines, B. "Rational curves and (0, 2)deformations." Journal of Geometry and Physics 88 (February 2015): 115. Full Text
 Aspinwall, PS, Melnikov, IV, and Plesser, MR. "(0,2) elephants." Journal of High Energy Physics 2012, no. 1 (2012). Full Text
 Aspinwall, PS, and Morrison, DR. "Quivers from Matrix Factorizations." Communications in Mathematical Physics 313, no. 3 (2012): 607633. Full Text
 Aspinwall, PS, and Plesser, MR. "Decompactifications and massless Dbranes in hybrid models." Journal of High Energy Physics 2010, no. 7 (2010). Full Text
 Aspinwall, PS. "Topological Dbranes and commutative algebra." Communications in Number Theory and Physics 3, no. 3 (2009): 445474.
 Aspinwall, PS, Maloney, A, and Simons, A. "Black hole entropy, marginal stability and mirror symmetry." Journal of High Energy Physics 2007, no. 7 (2007). Full Text
 Aspinwall, PS. "LandauGinzburg to CalabiYau dictionary for Dbranes." Journal of Mathematical Physics 48, no. 8 (2007). Full Text
 Aspinwall, PS, and Fidkowski, LM. "Superpotentials for quiver gauge theories." Journal of High Energy Physics 2006, no. 10 (2006). Full Text
 Aspinwall, PS, and Katz, S. "Computation of superpotentials for Dbranes." Communications in Mathematical Physics 264, no. 1 (2006): 227253. Full Text
 Aspinwall, PS, Horja, RP, and Karp, RL. "Massless Dbranes on CalabiYau threefolds and monodromy." Communications in Mathematical Physics 259, no. 1 (2005): 4569. Full Text
 Aspinwall, PS, and Kallosh, R. "Fixing all moduli for Mtheory on K3×K3." Journal of High Energy Physics , no. 10 (2005): 120. Full Text
 Aspinwall, PS, and Melnikov, IV. "Dbranes on vanishing del Pezzo surfaces." Journal of High Energy Physics 8, no. 12 (2004): 901930.
 Aspinwall, PS. "The breakdown of topology at small scales." Journal of High Energy Physics 8, no. 7 (2004): 453463.
 Aspinwall, PS, and Karp, RL. "Solitons in SeibergWitten theory and Dbranes in the derived category." Journal of High Energy Physics 7, no. 4 (2003): 11191137.
 Aspinwall, PS. "A point's point of view of stringy geometry." Journal of High Energy Physics 7, no. 1 (2003): 1731.
 Aspinwall, PS, and Douglas, MR. "Dbrane stability and monodromy." Journal of High Energy Physics 6, no. 5 (2002): 739773.
 Aspinwall, PS, and Lawrence, A. "Derived categories and zerobrane stability." Journal of High Energy Physics 5, no. 8 (2001): XIV26.
 Aspinwall, PS, and Plesser, MR. "Dbranes, discrete torsion and the McKay correspondence." Journal of High Energy Physics 5, no. 2 (2001): XIX25.
 Aspinwall, PS. "Some navigation rules for Dbrane monodromy." Journal of Mathematical Physics 42, no. 12 (2001): 55345552. Full Text
 Aspinwall, PS, Katz, S, and Morrison, DR. "Lie groups, CalabiYau threefolds, and Ftheory." Advances in Theoretical and Mathematical Physics 4, no. 1 (2000): 124.
 Aspinwall, PS, and Plesser, MR. "Heterotic string corrections from the dual typeII string." Journal of High Energy Physics 4, no. 4 (2000): XXXIV21.
 Aspinwall, PS. "A note on the equivalence of Vafa's and Douglas's picture of discrete torsion." Journal of High Energy Physics 4, no. 12 (2000): XXXVIII6.
 Aspinwall, PS, and Plesser, MR. "Tduality can fail." Journal of High Energy Physics 3, no. 8 (1999): XI18.
 Aspinwall, PS, and Donagi, RY. "The heterotic string, The tangent bundle and derived categories." Advances in Theoretical and Mathematical Physics 2, no. 5 (1998): 10411074.
 Aspinwall, PS, and Morrison, DR. "Nonsimplyconnected gauge groups and rational points on elliptic curves." Journal of High Energy Physics 1998, no. 7 (1998): XXII15.
 Aspinwall, PS. "Aspects of the hypermultiplet moduli space in string duality." Journal of High Energy Physics 2, no. 4 (1998): XXIX26.
 Aspinwall, PS, and Morrison, DR. "Pointlike instantons on K3 orbifolds." Nuclear Physics B 503, no. 3 (1997): 533564.
 Aspinwall, PS. "Pointlike instantons and the Spin(32)/ℤ_{2} heterotic string." Nuclear Physics B 496, no. 12 (1997): 149176.
 Aspinwall, PS, Morrison, DR, and Gross, M. "Stable singularities in string theory." Communications in Mathematical Physics 178, no. 1 (1996): 115134.
 Aspinwall, PS, and Gross, M. "Heteroticheterotic string duality and multiple K3 fibrations." Physics Letters, Section B: Nuclear, Elementary Particle and HighEnergy Physics 382, no. 12 (1996): 8188.
 Aspinwall, PS, and Louis, J. "On the ubiquity of K3 fibrations in string duality." Physics Letters, Section B: Nuclear, Elementary Particle and HighEnergy Physics 369, no. 34 (1996): 233242.
 Aspinwall, PS. "Some relationships between dualities in string theory." Nuclear Physics B  Proceedings Supplements 46, no. 13 (1996): 3038. Full Text
 Aspinwall, PS. "Enhanced gauge symmetries and CalabiYau threefolds." Physics Letters, Section B: Nuclear, Elementary Particle and HighEnergy Physics 371, no. 34 (1996): 231237.
 Aspinwall, PS. "An N = 2 dual pair and a phase transition." Nuclear Physics B 460, no. 1 (1996): 5776. Full Text
 Aspinwall, PS, and Greene, BR. "On the geometric interpretation of N = 2 superconformal theories." Nuclear Physics, Section B 437, no. 1 (1995): 205227. Full Text
 Aspinwall, PS, and Morrison, DR. "Uduality and integral structures." Physics Letters B 355, no. 12 (1995): 141149. Full Text
 Aspinwall, PS. "Enhanced gauge symmetries and K3 surfaces." Physics Letters B 357, no. 3 (1995): 329334. Full Text
 Aspinwall, PS, Greene, BR, and Morrison, DR. "CalabiYau moduli space, mirror manifolds and spacetime topology change in string theory." Nuclear Physics B 416, no. 2 (1994): 414480.
 Aspinwall, PS, Greene, BR, and Morrison, DR. "Spacetime topology change and stringy geometry a." Journal of Mathematical Physics 35, no. 10 (1994): 53215337.
 Aspinwall, PS, Greene, BR, and Morrison, DR. "Measuring small distances in N = 2 sigma models." Nuclear Physics, Section B 420, no. 12 (1994): 184242. Full Text
 Aspinwall, PS, and Morrison, DR. "Chiral rings do not suffice: N=(2,2) theories with nonzero fundamental group." Physics Letters B 334, no. 12 (1994): 7986. Full Text
 Aspinwall, PS. "Minimum distances in nontrivial string target spaces." Nuclear Physics B 431, no. 12 (1994): 7896.
 Aspinwall, PS, Greene, BR, and Morrison, DR. "Multiple mirror manifolds and topology change in string theory." Physics Letters B 303, no. 34 (1993): 249259. Full Text
 Aspinwall, PS, Morrison, DR, and Greene, BR. "The monomialdivisor mirror map." International Mathematics Research Notices 1993, no. 12 (January 1, 1993): 319337. Full Text
 Aspinwall, PS, and Morrison, DR. "Topological field theory and rational curves." Communications in Mathematical Physics 151, no. 2 (1993): 245262. Full Text
 Aspinwall, PS, and Lütken, CA. "Quantum algebraic geometry of superstring compactifications." Nuclear Physics, Section B 355, no. 2 (1991): 482510. Full Text
 Aspinwall, PS, and Lütken, CA. "Geometry of mirror manifolds." Nuclear Physics B 353, no. 2 (1991): 427461.
 Aspinwall, P. "(2, 2)Superconformal field theories near orbifold points." Communications in Mathematical Physics 128, no. 3 (1990): 593611. Full Text
 Aspinwall, PS, Lütken, CA, and Ross, GG. "Construction and couplings of mirror manifolds." Physics Letters, Section B: Nuclear, Elementary Particle and HighEnergy Physics 241, no. 3 (1990): 373380.
 ASPINWALL, PS, GREENE, BR, KIRKLIN, KH, and MIRON, PJ. "SEARCHING FOR 3GENERATION CALABIYAU MANIFOLDS." NUCLEAR PHYSICS B 294, no. 1 (November 23, 1987): 193222. Full Text Link to Item
 Aspinwall, PS, Greene, BR, Kirklin, KH, and Miron, PJ. "Searching for threegeneration CalabiYau manifolds." Nuclear Physics, Section B 294, no. C (1987): 193222. Full Text
 Addington, N, and Aspinwall, PS. "Categories of Massless DBranes and del Pezzo Surfaces." J. High Energy Phys. 7(176):39pp., 2013 . Full Text Link to Item
 Aspinwall, PS, Greene, BR, and Morrison, DR. "The MonomialDivisor Mirror Map." Internat. Math. Res. Notices (1993), 319337 . Link to Item
 Aspinwall, PS, and Gross, M. "The SO(32) Heterotic String on a K3 Surface." Phys.Lett. B 387: 735742. Full Text Link to Item
 Aspinwall, PS, and Kallosh, R. "Fixing All Moduli for MTheory on K3xK3." JHEP 0510: 001. Full Text Link to Item
 Aspinwall, PS, and Karp, RL. "Solitons in SeibergWitten Theory and Dbranes in the Derived Category." JHEP 0304: 049. Full Text Link to Item
 Aspinwall, PS, and Melnikov, IV. "DBranes on Vanishing del Pezzo Surfaces." JHEP 0412: 042. Full Text Link to Item
 Aspinwall, PS, and Plesser, MR. "Dbranes, Discrete Torsion and the McKay Correspondence." JHEP 0102: 009. Full Text Link to Item
 Aspinwall, PS, and Plesser, MR. "Heterotic String Corrections from the Dual Type II String." JHEP 0004: 025. Full Text Link to Item
 Aspinwall, PS, and Plesser, MR. "TDuality Can Fail." JHEP 9908: 001. Full Text Link to Item
 Aspinwall, PS, and Plesser, MR. "Decompactifications and Massless DBranes in Hybrid Models." JHEP 1007: 078. Full Text Link to Item
 Aspinwall, PS. "Compactification, Geometry and Duality: N=2." Link to Item
 Aspinwall, PS. "A Point's Point of View of Stringy Geometry." JHEP 0301: 002. Full Text Link to Item
 Aspinwall, PS. "The Breakdown of Topology at Small Scales." JHEP 0407: 021. Full Text Link to Item
 Aspinwall, PS. "A McKayLike Correspondence for (0,2)Deformations." Link to Item
 Aspinwall, PS. "DBranes on CalabiYau Manifolds." Full Text Link to Item

 Teaching & Mentoring

Recent Courses
 MATH 404: Mathematical Cryptography 2017
 MATH 431: Advanced Calculus I 2017
 MATH 492: Independent Study 2017
 MATH 371: Combinatorics 2016
 MATH 391: Independent Study 2016
 MATH 491: Independent Study 2016
 MATH 612: Algebraic Topology II 2016
 PHYSICS 491: Independent Study: Advanced Topics 2016
 MATH 611: Algebraic Topology I 2015
 Scholarly, Clinical, & Service Activities

Presentations & Appearances
 Bad Conformal Field Theories. Physics Department, University of Pennsylvania. April 18, 2016 2016
 Discriminants and Mirror Symmetry. Homological Mirror Symmetry. BIRS . March 9, 2016 2016
 Discriminants and Mirror Symmetry. F Theory at 20. CalTech. February 25, 2016 2016
 Massless Dbranes and Discriminants. Stanford University. December 21, 2015 2015
 The Kahler Moduli Space of CalabiYau Manifolds. December 22, 2013 2013
 Exoflops and Extremal Transitions. December 17, 2013 2013
 Monodromy and Collapsing del Pezzo Surfaces. June 11, 2013 2013
 The topological Bmodel and superpotentials. August 14, 2012 2012
 DBranes on CalabiYau Threefolds. July 9, 2012 2012
 DBranes on CalabiYau Threefolds. July 3, 2012 2012
 Linear sigma models and (0,2) models. May 14, 2012 2012
 A (0,2) McKay Correspondence. December 12, 2011 2011
 A (0,2) McKay Correspondence. November 5, 2011 2011
 A Study of (0,2) Deformations of (2,2) Theories. June 9, 2011 2011
 Quivers and Matrix Factorizations. May 18, 2011 2011
 A Study of (0,2) Deformations of (2,2) Theories. May 9, 2011 2011
 DBranes, Toric Geometry and Matrix Factorizations. March 18, 2011 2011
 Can Instantons Kill H1(End(T)) Singlets?. December 20, 2010 2010
 String Theory and the McKay Correspondence. June 15, 2009 2009
 Probing CalabiYau Geometry with DBranes. March 30, 2009 2009
 Geometry and String Theory. February 6, 2009 2009
 Probing CalabiYau Geometry with DBranes. January 14, 2009 2009
 Probing CalabiYau Geometry with DBranes. November 6, 2008 2008
 Probing CalabiYau Geometry with DBranes. October 20, 2008 2008
 BType DBranes on CalabiYau Manifolds. July 21, 2008 2008
 NonCommutative Resolutions and Toric Geometry. May 12, 2008 2008
 Computations in String Theory with Macaulay 2. March 17, 2008 2008

Service to the Profession
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