Contents

Foreword x1

Summary of the principal lectures xiii

An overview of Lie's line-sphere correspondence

R. MILSON

1

Application of Lie group analysis to a mathematical model which describes

HIV transmission

V.

ToRRISI AND M.

C. Nucci 11

Geometry and PDE on the Heisenberg group: a case study

RICHARD BEALS

21

Invariant evolutions of curves and surfaces and completely integrable

Hamiltonian systems

G.

MARl BEFFA

29

On the fixed points of the Toda hierarchy

BARBARA A. SHIPMAN

39

Group invariant solutions in mathematical physics and differential geometry

I.

M. ANDERSON, M. E. FELS, AND

C. G.

TORRE

51

Discrete symmetries of differential equations

P. E. HYDON

61

Integrable geometric evolution equations for curves

THOMAS A. IVEY

71

On integrability of evolution equations and representation theory

JAN A. SANDERS AND JING PING WANG

85

Symmetry groups, nonlinear partial differential equations, and generalized

functions

MICHAEL 0BERGUGGENBERGER

101

Lie symmetries of differential-difference equations

R. HERNANDEZ HEREDERO 111

On a variational complex for difference equations

ELIZABETH

L.

MANSFIELD AND PETER

E.

HYDON

121

vii