| Katrina D. Barron Office: ATTENTION!!! My office has changed to 276C Hurley!!!!!! Phone: 574-631-3981 E-mail: kbarron@nd.edu Mailing Address: 255 Hurley Hall |
i miei bambini |
Current Courses:
Spring 2008 Semester:
Math 10560 Section 03 Calculus II. Click here for the course webpage.
Math 80220 Section 01 Topics in Algebra II: Vertex Operator Algebras and Conformal Field Theory.
Click here for the course webpage.
Research: My research focuses on vertex operator
superalgebras and the algebraic and geometric foundations of
superconformal field theory.
Conformal field theory (CFT), or more specifically, string theory, and related superconformal field theories (SCFTs) are the most promising attempts at developing a physical theory that combines all fundamental interactions of particles, including gravity. The ``super" refers to an assumed symmetry between bosons (integral spin particles with symmetric wave functions) and fermions (half integral spin particles with anti-symmetric wave functions).
The geometry of CFT and SCFT extends the use of Feynman diagrams,
describing the interactions of point particles whose
propagation in time sweeps out a line in space-time, to one-dimensional
strings or superstrings whose propagation in time
sweeps out a two-dimensional surface or supersurface called a
``worldsheet".
Much of my research involves the study of relationships between the worldsheet geometry of CFT and SCFT and properties of the algebras of correlation functions of the particle interactions. For genus-zero holomorphic CFT and SCFT these algebras are called vertex operator superalgebras.
Selected Publications:
K. Barron, On axiomatic aspects of N=2 vertex superalgebras with odd formal variables, and deformations of N=1 vertex superalgebras, submitted.
K. Barron, The moduli space of N=2 super-Riemann spheres with tubes, Commun. in Contemp. Math., vol. 9 (2007), 857-940.
K. Barron, Y.-Z. Huang, J. Lepowsky, An equivalence of two constructions of permutation-twisted modules for lattice vertex operator algebras, J. Pure and Appl. Algebra, vol. 210 (2007), 797-826.
K. Barron, Superconformal change of variables for N=1 Neveu-Schwarz vertex operator superalgebras, J. of Algebra, vol. 277 (2004), 717-764.
K. Barron, The notion of N=1 supergeometric vertex operator superalgebra and the isomorphism theorem, Commun. in Contemp. Math., vol. 5 (2003), 481-567.
K. Barron, The moduli space of N=1 superspheres with tubes and the sewing operation, Memoirs of the AMS, vol. 162, no. 772, (2003).
K. Barron, C. Dong, G. Mason, Twisted sectors for tensor product vertex operator algebras associated to permutation groups, Commun. in Math. Phys., vol. 227 (2002), 349-384.
K. Barron, Y.-Z. Huang, J. Lepowsky, Factorization of formal exponentials and uniformization, J. of Algebra, vol. 228 (2000), 551-579.
K. Barron, N=1 Neveu-Schwarz vertex operator superalgebras over Grassmann algebras and with odd formal variables, in ``Representations and Quantizations: Proceedings of the International Conference on Representation Theory, 1998", ed. by J. Wang and Z. Lin, China Higher Education Press & Springer-Verlag, Beijing, 2000, 9-36.
Graduate Ph.D. and Undergraduate Honors Students:
Keith Hubbard, Ph.D. Student.
-Ph.D. Spring 2005.
-Dissertation: The notion of vertex operator
coalgebra: A construction and geometric interpretation.
-Papers: The
notion of vertex operator coalgebra and a geometric construction,
Commun. in Alg., vol. 34, (2006), no. 5, 1541-1589.
Constructions of vertex
operator coalgebras via vertex operator algebras, J.
of Algebra, vol. 294, (2005), 278-293.
Andrew Lynch, Senior Honors Student.
-Honors B.A. Spring 2003.
-Senior Honors Thesis: Aspects of the classification
of finite simple groups.
Conferences:
Groups and Algebras in M-Theory, Rutgers University, NJ, 31 May - 4 June, 2005.
Activism:
Never doubt that a small group of thoughtful,
committed citizens can change the world. Indeed, it is the only thing
that ever has.
- Margaret Mead
Legislative Information
on the Net -- How are your elected officials voting?
Contact your elected officials and take a look at the Congressional
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Current events and venues for contacting your local officials and being
active in your community and the world: Act For
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through Veterans for Peace.
In particular, the Veterans
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