Special Session: "Association Schemes: 1973--2003"

AMS 2003 Fall Southeastern Section Meeting

Chapel Hill, NC, October 24-25, 2003

The theory of association schemes has its roots in the statistical design of experiments and in the study of groups acting on finite sets. A founder of the theory, Raj Chandra Bose, served on the Chapel Hill faculty from 1949 to 1971. In 1973, an important new role for association schemes emerged through the work of Philippe Delsarte and others: certain association schemes were shown to play a central part in the study of error-correcting codes.

Theme

Current research in the area includes:

• statistical design of experiments, PBIBD's
• finite group actions, character theory
• distance-regular graphs, P- and Q-polynomial association schemes
• extremal graph theory
• knot theory, spin models, Type II matrices
• geometries, buildings, etc.
• coding theory
• combinatorial designs

Speakers

• Paul Terwilliger, University of Wisconsin
  ``Tridiagonal pairs and the quantum affine algebra U<sub>q</sub>({\hat sl}<sub>2</sub>)''
• Mark MacLean, University of North Carolina at Asheville
  ``Taut distance-regular graphs of even diameter''
• John Caughman, Portland State University
  ``The Terwilliger algebra of a distance-regular graph that supports a spin model''
• Brian Curtin, University of South Florida
  ``Modular Leonard triples''
• Ada Chan, California Institute of Technology
  ``Type-II matrices, four-weight spin models and Nomura algebras''

• Paul-Hermann Zieschang, University of Texas at Brownsville
  ``A survey on the structure theory of association schemes''
• Andrew Woldar, Villanova University
  ``Amorphic association schemes, I. From folklore to foundation''
• Mikhail Klin, Ben-Gurion University of the Negev
  ``Amorphic association schemes, II. A positive answer on a question of Barlotti-Strambach''
• Sung Yell Song, Iowa State University
  ``Decompositions of an association scheme''
• Jianmin Ma, Colorado State University
  ``Some new 3-class association schemes''

• Rosemary Bailey, University of London
  ``Designs on association schemes''
• Malcolm Greig, Greig Consulting
  ``Some non-existence results for partially balanced incomplete block designs''
• Mohan Shrikhande, Central Michigan University
  ``Delsarte polynomials and designs''
• Tuvi Etzion, The Technion
  ``Perfect Codes in the Johnson Scheme''
• Jin Qian, General Bandwidth Corporation and Dijen Ray-Chaudhuri, Ohio State University
  ``Inequalities for association schemes''
• Chris Godsil, University of Waterloo
  ``Colouring graphs from association schemes''

• Paul Camion, Universite Pierre et Marie Curie (Paris 6)
  ``Open problems related to association schemes''
• Qing Xiang, University of Delaware
  ``Constructions of pseudocyclic association schemes''
• Vera Pless, University of Illinois at Chicago
  ``Explicit constructions of families of LDPC codes with girth at least six''
• Alexei Ashikhmin, Lucent Technologies
  ``Bounds on the distance distribution of a code of known size and minimum distance''
• Jack Koolen, Korean Advanced Institute of Science and Technology
  ``Completely regular binary codes''
• William Martin, Worcester Polytechnic Institute
  ``The biweight enumerator of a binary code and the subconstituent algebra of the hypercube''