Paul Stephen Aspinwall | Scholars@Duke

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

2:00 to 3:00pm each Friday
10:00 to 11:00am each Wednesday

Current Appointments & Affiliations

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

Contact Information

244 Physics Bldg, Durham, NC 27708
Box 90320, Durham, NC 27708-0320
psa@cgtp.duke.edu (919) 660-2874
http://www.cgtp.duke.edu/~psa

Background
Education, Training, & Certifications
- D.Phil., University of Oxford (United Kingdom) 1988
- B.A., University of Oxford (United Kingdom) 1985
Previous Appointments & Affiliations
- Interim Chair of the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2015
- Associate Chair of the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2010 - 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
- Sloan Research Fellowship-Physics. Alfred P. Sloan Foundation. 1999
Research
Selected Grants
- Moduli Spaces & String Theory awarded by National Science Foundation 2012 - 2017
- Geometry and Mathematical Physics of D-Branes awarded by National Science Foundation 2009 - 2014
- Algebraic Geometry and Quantum Field Theory of D-Branes awarded by National Science Foundation 2006 - 2011
- D-Brane Physics and Calabi-Yau Geometry awarded by National Science Foundation 2003 - 2007
- Focused Research Group: Calabi-Yau Manifolds and their Applications awarded by National Science Foundation 2000 - 2004
External Relationships
- SISSA - Trieste
Publications & Artistic Works
Selected Publications
- Academic Articles
  - Aspinwall, P. S., and M. R. Plesser. “General mirror pairs for gauged linear sigma models.” Journal of High Energy Physics 2015, no. 11 (November 1, 2015): 1–33. https://doi.org/10.1007/JHEP11(2015)029.
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  - Aspinwall, P. S. “Exoflops in two dimensions.” Journal of High Energy Physics 2015, no. 7 (July 31, 2015). https://doi.org/10.1007/JHEP07(2015)104.
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  - Aspinwall, P. S., and B. Gaines. “Rational curves and (0, 2)-deformations.” Journal of Geometry and Physics 88 (February 1, 2015): 1–15. https://doi.org/10.1016/j.geomphys.2014.09.012.
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  - Aspinwall, P. S. “A McKay-like correspondence for (0, 2)-deformations.” Advances in Theoretical and Mathematical Physics 18, no. 4 (January 1, 2014): 761–97. https://doi.org/10.4310/ATMP.2014.v18.n4.a1.
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  - Addington, N., and P. S. Aspinwall. “Categories of massless D-branes and del Pezzo surfaces.” Journal of High Energy Physics 2013, no. 7 (August 19, 2013). https://doi.org/10.1007/JHEP07(2013)176.
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  - Aspinwall, P. S., and D. R. Morrison. “Quivers from Matrix Factorizations.” Communications in Mathematical Physics 313, no. 3 (August 1, 2012): 607–33. https://doi.org/10.1007/s00220-012-1520-1.
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  - Aspinwall, P. S., I. V. Melnikov, and M. Ronen Plesser. “(0,2) elephants.” Journal of High Energy Physics 2012, no. 1 (February 27, 2012). https://doi.org/10.1007/JHEP01(2012)060.
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  - Aspinwall, P. S., and M. R. Plesser. “Decompactifications and massless D-branes in hybrid models.” Journal of High Energy Physics 2010, no. 7 (January 1, 2010). https://doi.org/10.1007/JHEP07(2010)078.
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  - Aspinwall, P. S. “Topological D-branes and commutative algebra.” Communications in Number Theory and Physics 3, no. 3 (January 1, 2009): 445–74. https://doi.org/10.4310/CNTP.2009.v3.n3.a1.
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  - Aspinwall, P. S. “Landau-Ginzburg to Calabi-Yau dictionary for D-branes.” Journal of Mathematical Physics 48, no. 8 (September 7, 2007). https://doi.org/10.1063/1.2768185.
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  - Aspinwall, P. S., A. Maloney, and A. Simons. “Black hole entropy, marginal stability and mirror symmetry.” Journal of High Energy Physics 2007, no. 7 (July 1, 2007). https://doi.org/10.1088/1126-6708/2007/07/034.
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  - Aspinwall, P. S., and L. M. Fidkowski. “Superpotentials for quiver gauge theories.” Journal of High Energy Physics 2006, no. 10 (October 1, 2006). https://doi.org/10.1088/1126-6708/2006/10/047.
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  - Aspinwall, P. S., and S. Katz. “Computation of superpotentials for D-branes.” Communications in Mathematical Physics 264, no. 1 (May 1, 2006): 227–53. https://doi.org/10.1007/s00220-006-1527-6.
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  - Aspinwall, P. S., R. P. Horja, and R. L. Karp. “Massless D-branes on Calabi-Yau threefolds and monodromy.” Communications in Mathematical Physics 259, no. 1 (October 1, 2005): 45–69. https://doi.org/10.1007/s00220-005-1378-6.
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  - Aspinwall, P. S., and R. Kallosh. “Fixing all moduli for M-theory on K3×K3.” Journal of High Energy Physics, no. 10 (October 1, 2005): 1–20. https://doi.org/10.1088/1126-6708/2005/10/001.
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  - Aspinwall, P. S. “D-branes on Calabi-Yau manifolds,” January 1, 2005, 1–152. https://doi.org/10.1142/9789812775108_0001.
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  - Aspinwall, P. S., and I. V. Melnikov. “D-branes on vanishing del Pezzo surfaces.” Journal of High Energy Physics 8, no. 12 (December 1, 2004): 901–30. https://doi.org/10.1088/1126-6708/2004/12/042.
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  - Aspinwall, P. S. “The breakdown of topology at small scales.” Journal of High Energy Physics 8, no. 7 (July 1, 2004): 453–63. https://doi.org/10.1088/1126-6708/2004/07/021.
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  - Aspinwall, P. S. “The breakdown of topology at small scales.” Journal of High Energy Physics 8, no. 7 (2004): 453–63.
  - Aspinwall, P. S., and I. V. Melnikov. “D-branes on vanishing del Pezzo surfaces.” Journal of High Energy Physics 8, no. 12 (2004): 901–30.
  - Aspinwall, P. S., and R. L. Karp. “Solitons in Seiberg-Witten theory and D-branes in the derived category.” Journal of High Energy Physics 7, no. 4 (April 1, 2003): 1119–37. https://doi.org/10.1088/1126-6708/2003/04/049.
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  - Aspinwall, P. S. “A point's point of view of stringy geometry.” Journal of High Energy Physics 7, no. 1 (January 1, 2003): 17–31. https://doi.org/10.1088/1126-6708/2003/01/002.
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  - Aspinwall, P. S. “A point's point of view of stringy geometry.” Journal of High Energy Physics 7, no. 1 (2003): 17–31.
  - Aspinwall, P. S., and R. L. Karp. “Solitons in Seiberg-Witten theory and D-branes in the derived category.” Journal of High Energy Physics 7, no. 4 (2003): 1119–37.
  - Aspinwall, P. S., and M. R. Douglas. “D-brane stability and monodromy.” Journal of High Energy Physics 6, no. 5 (May 1, 2002): 739–73. https://doi.org/10.1088/1126-6708/2002/05/031.
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  - Aspinwall, P. S. “Some navigation rules for D-brane monodromy.” Journal of Mathematical Physics 42, no. 12 (December 1, 2001): 5534–52. https://doi.org/10.1063/1.1409963.
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  - Aspinwall, P. S., and A. Lawrence. “Derived categories and zero-brane stability.” Journal of High Energy Physics 5, no. 8 (January 1, 2001): 1–26. https://doi.org/10.1088/1126-6708/2001/08/004.
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  - Aspinwall, P. S., and M. R. Plesser. “D-branes, discrete torsion and the McKay correspondence.” Journal of High Energy Physics 5, no. 2 (January 1, 2001). https://doi.org/10.1088/1126-6708/2001/02/009.
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  - Aspinwall, P. S., and M. R. Plesser. “D-branes, discrete torsion and the McKay correspondence.” Journal of High Energy Physics 5, no. 2 (2001): XIX–25.
  - Aspinwall, P. S. “A note on the equivalence of Vafa's and Douglas's picture of discrete torsion.” Journal of High Energy Physics 4, no. 12 (January 1, 2000). https://doi.org/10.1088/1126-6708/2000/12/029.
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  - Aspinwall, P. S., S. Katz, and D. R. Morrison. “Lie groups, Calabi-Yau threefolds, and F-theory.” Advances in Theoretical and Mathematical Physics 4, no. 1 (January 1, 2000): 95–126. https://doi.org/10.4310/atmp.2000.v4.n1.a2.
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  - Aspinwall, P. S., and M. R. Plesser. “Heterotic string corrections from the dual type-II string.” Journal of High Energy Physics 4, no. 4 (2000): XXXIV–21.
  - Aspinwall, P. S., and M. Ronen Plesser. “Heterotic string corrections from the dual type-II string.” Journal of High Energy Physics 4, no. 4 (January 1, 2000). https://doi.org/10.1088/1126-6708/2000/04/025.
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  - Aspinwall, Paul S. “Compactification, Geometry and Duality: N=2,” December 31, 1999.
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  - Aspinwall, P. S., and M. R. Plesser. “T-duality can fail.” Journal of High Energy Physics 3, no. 8 (January 1, 1999). https://doi.org/10.1088/1126-6708/1999/08/001.
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  - Aspinwall, P. S., and M. R. Plesser. “T-duality can fail.” Journal of High Energy Physics 3, no. 8 (1999): XI–18.
  - Aspinwall, P. S. “Aspects of the hypermultiplet moduli space in string duality.” Journal of High Energy Physics 2, no. 4 (January 1, 1998). https://doi.org/10.1088/1126-6708/1998/04/019.
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  - Aspinwall, P. S., and D. R. Morrison. “Non-simply-connected gauge groups and rational points on elliptic curves.” Journal of High Energy Physics 1998, no. 7 (January 1, 1998). https://doi.org/10.1088/1126-6708/1998/07/012.
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  - Aspinwall, P. S., and R. Y. Donagi. “The heterotic string, The tangent bundle and derived categories.” Advances in Theoretical and Mathematical Physics 2, no. 5 (January 1, 1998): 1041–74. https://doi.org/10.4310/ATMP.1998.v2.n5.a4.
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  - Aspinwall, P. S., and D. R. Morrison. “Point-like instantons on K3 orbifolds.” Nuclear Physics B 503, no. 3 (October 20, 1997): 533–64. https://doi.org/10.1016/S0550-3213(97)00516-6.
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  - Aspinwall, P. S. “Point-like instantons and the Spin(32)/ℤ2 heterotic string.” Nuclear Physics B 496, no. 1–2 (July 7, 1997): 149–76. https://doi.org/10.1016/S0550-3213(97)00232-0.
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  - Aspinwal, P. S., and M. Gross. “The SO(32) heterotic string on a K3 surface.” Physics Letters, Section B: Nuclear, Elementary Particle and High Energy Physics 387, no. 4 (October 31, 1996): 735–42. https://doi.org/10.1016/0370-2693(96)01095-7.
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  - Aspinwall, P. S., and M. Gross. “Heterotic-heterotic string duality and multiple K3 fibrations.” Physics Letters, Section B: Nuclear, Elementary Particle and High Energy Physics 382, no. 1–2 (August 1, 1996): 81–88. https://doi.org/10.1016/0370-2693(96)00551-5.
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  - Aspinwall, P. S., D. R. Morrison, and M. Gross. “Stable singularities in string theory.” Communications in Mathematical Physics 178, no. 1 (May 1, 1996): 115–34. https://doi.org/10.1007/BF02104911.
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  - Aspinwall, P. S. “Enhanced gauge symmetries and Calabi-Yau threefolds.” Physics Letters, Section B: Nuclear, Elementary Particle and High Energy Physics 371, no. 3–4 (March 28, 1996): 231–37. https://doi.org/10.1016/0370-2693(96)00003-2.
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  - Aspinwall, P. S., and J. Louis. “On the ubiquity of K3 fibrations in string duality.” Physics Letters, Section B: Nuclear, Elementary Particle and High Energy Physics 369, no. 3–4 (February 29, 1996): 233–42. https://doi.org/10.1016/0370-2693(95)01541-8.
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  - Aspinwall, P. S. “An N = 2 dual pair and a phase transition.” Nuclear Physics B 460, no. 1 (January 29, 1996): 57–76. https://doi.org/10.1016/0550-3213(95)00611-7.
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  - Aspinwall, P. S. “Some relationships between dualities in string theory.” Nuclear Physics B Proceedings Supplements 46, no. 1–3 (January 1, 1996): 30–38. https://doi.org/10.1016/0920-5632(96)00004-7.
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  - Aspinwall, P. S. “Enhanced gauge symmetries and K3 surfaces.” Physics Letters B 357, no. 3 (September 7, 1995): 329–34. https://doi.org/10.1016/0370-2693(95)00957-M.
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  - Aspinwall, P. S., and D. R. Morrison. “U-duality and integral structures.” Physics Letters B 355, no. 1–2 (July 27, 1995): 141–49. https://doi.org/10.1016/0370-2693(95)00745-7.
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  - Aspinwall, P. S., and B. R. Greene. “On the geometric interpretation of N = 2 superconformal theories.” Nuclear Physics, Section B 437, no. 1 (March 6, 1995): 205–27. https://doi.org/10.1016/0550-3213(94)00571-U.
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  - Aspinwall, P. S. “Minimum distances in non-trivial string target spaces.” Nuclear Physics, Section B 431, no. 1–2 (December 5, 1994): 78–96. https://doi.org/10.1016/0550-3213(94)90098-1.
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  - Aspinwall, P. S., and D. R. Morrison. “Chiral rings do not suffice: N=(2,2) theories with nonzero fundamental group.” Physics Letters B 334, no. 1–2 (August 11, 1994): 79–86. https://doi.org/10.1016/0370-2693(94)90594-0.
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  - Aspinwall, P. S., B. R. Greene, and D. R. Morrison. “Measuring small distances in N = 2 sigma models.” Nuclear Physics, Section B 420, no. 1–2 (May 30, 1994): 184–242. https://doi.org/10.1016/0550-3213(94)90379-4.
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  - Aspinwall, P. S., B. R. Greene, and D. R. Morrison. “Calabi-Yau moduli space, mirror manifolds and spacetime topology change in string theory.” Nuclear Physics, Section B 416, no. 2 (March 28, 1994): 414–80. https://doi.org/10.1016/0550-3213(94)90321-2.
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  - Aspinwall, P. S., B. R. Greene, and D. R. Morrison. “Space-time topology change and stringy geometry a.” Journal of Mathematical Physics 35, no. 10 (January 1, 1994): 5321–37. https://doi.org/10.1063/1.530754.
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  - ASPINWALL, P. S., B. R. GREENE, and D. R. MORRISON. “THE MONOMIAL-DIVISOR MIRROR MAP.” Duke Mathematical Journal 72, no. 3 (December 1, 1993): 319–37.
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  - Aspinwall, P. S., B. R. Greene, and D. R. Morrison. “Multiple mirror manifolds and topology change in string theory.” Physics Letters B 303, no. 3–4 (April 15, 1993): 249–59. https://doi.org/10.1016/0370-2693(93)91428-P.
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  - Aspinwall, P. S., D. R. Morrison, and B. R. Greene. “The monomial-divisor mirror map.” International Mathematics Research Notices 1993, no. 12 (January 1, 1993): 319–37. https://doi.org/10.1155/S1073792893000376.
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  - Aspinwall, P. S., and D. R. Morrison. “Topological field theory and rational curves.” Communications in Mathematical Physics 151, no. 2 (January 1, 1993): 245–62. https://doi.org/10.1007/BF02096768.
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  - Aspinwall, P. S., and C. A. Lütken. “Quantum algebraic geometry of superstring compactifications.” Nuclear Physics, Section B 355, no. 2 (May 20, 1991): 482–510. https://doi.org/10.1016/0550-3213(91)90123-F.
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  - Aspinwall, P. S., and C. A. Lütken. “Geometry of mirror manifolds.” Nuclear Physics, Section B 353, no. 2 (April 15, 1991): 427–61. https://doi.org/10.1016/0550-3213(91)90343-V.
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  - Aspinwall, P. S., C. A. Lütken, and G. G. Ross. “Construction and couplings of mirror manifolds.” Physics Letters B 241, no. 3 (May 17, 1990): 373–80. https://doi.org/10.1016/0370-2693(90)91659-Y.
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  - Aspinwall, P. “(2, 2)-Superconformal field theories near orbifold points.” Communications in Mathematical Physics 128, no. 3 (March 1, 1990): 593–611. https://doi.org/10.1007/BF02096875.
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  - Aspinwall, P. S., B. R. Greene, K. H. Kirklin, and P. J. Miron. “Searching for three-generation Calabi-Yau manifolds.” Nuclear Physics, Section B 294, no. C (January 1, 1987): 193–222. https://doi.org/10.1016/0550-3213(87)90579-7.
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- Book Sections
  - Aspinwall, P. S. “Some applications of commutative algebra to string theory.” In Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday, 25–56, 2013. https://doi.org/10.1007/978-1-4614-5292-8_2.
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Teaching & Mentoring
Recent Courses
- MATH 421: Differential Geometry 2023
- MATH 603: Representation Theory 2023
- MATH 722: Differential Geometry 2023
- PHYSICS 603: Representation Theory 2023
- MATH 527: General Relativity 2022
- MATH 590-02: Advanced Special Topics in Mathematics 2022
- PHYSICS 590: Selected Topics in Theoretical Physics 2022
- PHYSICS 622: General Relativity 2022
- MATH 333: Complex Analysis 2021
- MATH 421: Differential Geometry 2021
- MATH 722: Differential Geometry 2021
- MATH 733: Complex Analysis 2021
Scholarly, Clinical, & Service Activities
Presentations & Appearances
Service to the Profession

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Education, Training, & Certifications

Previous Appointments & Affiliations

Awards & Honors

Selected Grants

External Relationships

Selected Publications

Academic Articles

Book Sections

Recent Courses

Presentations & Appearances

Service to the Profession