AMS 2003 Spring Central Sectional Meeting #985
April 4-6, Bloomington, IN

Special Session on Representations of Infinite Dimensional Lie Algebras and Mathematical Physics


 

General Information:

 

List of Participants, Titles of Talks, and Reference Links:
 

Iana Anguelova - University of Illinois at Urbana-Champaign
        Title: Quantum vertex algebras

Lev Borisov - University of Wisconsin
        Title: Chiral rings of vertex algebras of mirror symmetry

Michael Gekhtman - University of Notre Dame
        Title: Sklyanin Poisson brackets and refined Bruhat cells in real Grassmannians

Robert Griess, Jr. - University of Michigan
        Title: Framed VOAs and frame stabilizers

Yi-Zhi Huang - Rutgers University
        Title: Differential equations and conformal field theories -- Link to the pdf version of the paper; and link to the postscript version of the paper.
         Further references: Vertex Operator Algebras in Mathematics and Physics, to appear in:  Fields Institute Communications, ed. S. Berman, Y. Billig, Y.-Z. Huang and J. Lepowsky, Amer. Math. Soc., Providence, 24 pages; link to pdf version; and link to postcript version.
         Differential equations, duality and modular invariance, 69 pages, to appear; link to pdf version; and link to postscript version.
          Differential equations and conformal field theories,10 pages, to appear; link to pdf version; and link to postcript version.
 

Kate Hurley - University of South Carolina
        Title: Virasoro highest-weight vectors in vertex operator algebras-- Link to information provided by C. Schweigert on the interesting collection of exceptional Lie algebras appearing in Kate Hurley's talk.

James Lepowsky - Rutgers University
        Title: Intertwining operators for vertex operator algebras and recursions for q-series -- Link to first version of paper.

Tony Milas - University of Arizona
        Title: Logarithmic operators and vertex operator algebras

Kailash Misra - North Carolina State University
        Title: Bosonic realizations of higher level toroidal Lie algebras

David Radnell - Rutgers University
        Title: Schiffer variation in Teichm\"uller space and determinant line bundles

Michael Roitman - University of Michigan
        Title: Affinization of commutative algebras

Alistair Savage - Yale University
        Title: Bases of representations of type A affine Lie algebras via quiver varieties and statistical mechanics -- Link to paper.

Christoph Schweigert - RWTH Aachen
        Title: Algebras in Tensor categories and conformal field theory -- Link to postscript copy of transparancies.

Gaywalee Yamskulna - SUNY-Binghamton
        Title: C_2 cofiniteness of the vertex operator algebra V_L^+ when L is arank one lattice

Wenhua Zhao - Washington University in St. Louis
        Title: D-Log's and formal flows of analytic maps and rooted trees
 



Organizers:
 
Katrina D. Barron
Department of Mathematics
255 Hurley Hall
University of Notre Dame
Notre Dame, IN 46556
Phone: (574)631-3981
email: kbarron@nd.edu

Rinat Kedem
Department of Mathematics
University of Illinois at Urbana-Champaign
273 Altgeld Hall, MC-382
1409 W. Green Street
Urbana, IL 61801
Phone: (217)244-1350
email: rinat@math.uiuc.edu




Schedule:

            Friday, April 4th
               3:00 -   3:20  Iana Anguelova, Quantum vertex algebras
               3:30 -   3:50  Alistair Savage, Bases of representations of type A affine Lie algebras via quiver varieties and statistical mechanics
            4:00 -   4:20  David Radnell, Schiffer variation in Teichm\"uller space and determinant line bundles
               4:30 -   5:20  Lev Borisov, Chiral rings of vertex algebras of mirror symmetry
               5:40 -   6:30  AMS Invited Address

Saturday, April 5th
  8:30 -   9:20  Kailash Misra, Bosonic realizations of higher level toroidal Lie algebras
  9:30 -   9:50  Tony Milas, Logarithmic operators and vertex operator algebras
10:00 - 10:20  Wenhua Zhao, D-Log's and formal flows of analytic maps and rooted trees
10:30 - 11:20  James Lepowsky, Intertwining operators for vertex operator algebras and recursions for q-series
11:40 - 12:30  AMS Invited Address
LUNCH
  2:00 -   2:50  AMS Invited Address
  3:00 -   3:20  Gaywalee Yamskulna, C_2 cofiniteness of the vertex operator algebra V_L^+ when L is a rank one lattice
  3:30 -   3:50  Michael Roitman, Affinization of commutative algebras
  4:00 -   4:50  Robert Griess, Framed VOAs and frame stabilizers
  5:10 -   6:00  AMS Invited Address
RECEPTION HOSTED BY THE MATH DEPT OF INDIANA UNIVERSITY

Sunday, April 6th:
  9:30 - 10:20  Michael Gekhtman, Sklyanin Poisson brackets and refined Bruhat cells in real Grassmannians
10:30 - 11:20  Christoph Schweigert, Algebras in tensor categories and conformal field theory
11:30 - 11:50  Kate Hurley, Virasoro highest-weight vectors in vertex operator algebras
12:00 - 12:50  Yi-Zhi Huang, Differential equations and conformal field theories
 
 

Information provided by C. Schweigert on the interesting collection of exceptional Lie algebras appearing in Kate Hurley's talk:

The work of Deligne (in French):
P. Deligne, La s\'erie exceptionelle de groupes de Lie.
C.R.Acad.Sci. Paris (S\'erie I -- Math\'ematique) 322 (1996) 321

P. Deligne and R. de Man, La s\'erie exceptionelle de groupes de Lie II
C.R.Acad.Sci. Paris (S\'erie I -- Math\'ematique) 323 (1996) 577

Important checks on the conjectures (computer, using LiE):

A.M. Cohen and R. de Man, Computational evidence for Deligne's conjecture regarding exceptional Lie groups.
C.R.Acad.Sci. Paris (S\'erie I -- Math\'ematique) 322 (1996) 427

Intrigingly, the same series of exceptional Lie algebras appears in

Patrick Dorey, Andrew Pocklington, Roberto Tateo:
Integrable aspects of the scaling q-state Potts models I: bound states and bootstrap closure. Preprint available at http://arxiv.org/abs/hep-th/0208111
(contains also some references to highly unorthodox work of Cvitanovic about exceptional Lie groups).
 

 
Last updated April 15, 2003.