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
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