**Office Location:** 244 Physics Bldg, Durham, NC 27708**Office Phone:** (919) 660-2874**Email Address:** psa@cgtp.duke.edu**Web Page:** http://www.cgtp.duke.edu/~psa

**Specialties:**

Mathematical Physics

Geometry

**Education:**

D.Phil., University of Oxford (UK), 1988

Theoretical Elementary Particle Physics, Oxford, 1991

B.A., University of Oxford (UK), 1985

**Research Categories:** *String Theory*

**Research Description:**

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

**Teaching (Spring 2020):**

- Math 403.01,
*Advanced linear algebra*Synopsis- Physics 119, MW 01:25 PM-02:40 PM

- Math 703.01,
*Advanced linear algebra*Synopsis- Physics 119, MW 01:25 PM-02:40 PM

**Recent Publications**
(More Publications)

- Aspinwall, PS; Plesser, MR,
*General mirror pairs for gauged linear sigma models*, Journal of High Energy Physics, vol. 2015 no. 11 (November, 2015), pp. 1-33, Springer Nature [doi] [abs]. - Aspinwall, PS,
*Exoflops in two dimensions*, Journal of High Energy Physics, vol. 2015 no. 7 (July, 2015), Springer Nature [arXiv:1412.0612], [doi] [abs]. - Aspinwall, PS; Gaines, B,
*Rational curves and (0, 2)-deformations*, Journal of Geometry and Physics, vol. 88 (February, 2015), pp. 1-15, Elsevier BV [arXiv:1404.7802], [doi] [abs]. - Aspinwall, PS,
*A McKay-like correspondence for (0, 2)-deformations*, Advances in Theoretical and Mathematical Physics, vol. 18 no. 4 (January, 2014), pp. 761-797, International Press of Boston [1110.2524], [1110.2524v3], [doi] [abs]. - 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 (November, 2013), pp. 25-56, Springer New York [doi] [abs].

**Highlight:**

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 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)