TUTORIAL AND LECTURE TOPICS

Christine Bachoc, University of Bordeaux I, France

Tutorials

(T1) Introduction to coding theory

(T2) Introduction to representation theory of finite groups

Lecture: Semidefinite programming, harmonic analysis and coding theory

(L1) Introductory lecture: an overview

(L2) Tools from harmonic analysis

(L3) Explicit computations of invariant positive definite functions

(L4) SDP bounds for codes

Eiichi Bannai, Kyushu University, Japan: Algebraic combinatorics on spheres and
related topics

1. Spherical codes and designs

2. Algebraic combinatorics on spheres I

3. Algebraic combinatorics on spheres II

4. Toy models for D.H. Lehmer’s conjecture

5. Euclidean designs and coherent configurations

Henry Cohn, Microsoft Research, USA: Distribution of points on spheres

1. Introduction to spherical harmonics

2. Introduction to LP and SDP on spheres

3. Bounds for codes and packings

4. Energy minimization on spheres and applications I

5. Energy minimization on spheres and applications II

William Martin, Worcester Polytechnic Institute, USA:

Tutorials

(T1) The Hamming graph and the linear programming bound

(T2) Specific solutions to linear programming problems

Lectures: Terwilliger algebras in coding theory

(L1) The Bose-Mesner algebra of the Hamming graphs

(L2) The Terwilliger algebra of the n-cube and its positive semidefinite cone

(L3) Association schemes and its applications

Frank Vallentin, CWI, Amsterdam, Netherlands:

Tutorials

(T1) Introduction to SDP I

(T2) Introduction to SDP II

Lectures: Applications of semidefinite programming

(L1) Approximation algorithms for the maximum cut problem

(L2) Euclidean embeddings

(L3) Lower and upper bounds for Euclidean distortion

(L4) Algorithmic applications