Acknowledgments
I woul d lik e t o begi n b y payin g a specia l homag e t o th e memor y o f Rober t
Debever, m y teacher an d mento r a t th e Universit e Libr e de Bruxelles, unde r whos e
generous guidanc e I too k m y firs t step s i n th e pat h researc h mor e tha n twent y
two year s ago , an d whos e trus t an d suppor t mad e i t possibl e fo r m e t o pursu e a n
academic career . I woul d als o lik e t o tak e thi s opportunit y t o hono r th e memor y
of m y frien d an d colleagu e Robb y Gardner , wh o gav e s o muc h o f himsel f t o hi s
students an d t o hi s collaborators , an d fro m who m I learne d nearl y everythin g I
know abou t exterio r differentia l forms . The y ar e bot h deepl y misse d sinc e thei r
untimely death s i n 1998.
A significant portio n o f thi s monograp h i s base d o n join t researc h wit h Ia n
Anderson an d Ket i Tenenblat . I fee l ver y fortunat e t o hav e ha d th e opportunit y
to wor k wit h the m an d I woul d t o than k the m bot h fo r thes e wonderfu l year s
of collaboration . I ow e a tremendou s deb t o f gratitud e t o m y clos e frien d an d
collaborator o f many years, Peter Olver , whose deep insights, exemplary scholarshi p
and fundamenta l contribution s t o th e geometrica l stud y o f differentia l equation s
have had a deep influenc e o n my scientific development . Hi s exceptional generosit y
and war m friendshi p hav e bee n a constan t sourc e o f suppor t an d inspiratio n fo r
me. I woul d als o lik e t o than k Bil l Shadwic k fo r havin g introduce d m e t o th e
geometrical stud y o f differentia l equation s whil e I wa s a post-doctora l Fellow , fo r
having patiently taugh t m e the beautiful metho d o f equivalence of Elie Cartan, an d
for havin g share d man y o f his insight s wit h me .
I wis h t o expres s m y heartfel t gratitud e t o Joshu a Lesli e an d Thierr y Robar t
for th e magnificen t wor k tha t the y di d i n plannin g an d organizin g th e NSF-CBM S
Research Conferenc e o n th e Geometrica l Stud y o f Differentia l Equation s whic h
was hel d a t Howar d Universit y fro m Jun e 2 0 t o Jun e 25 , 2000 , an d t o Lucie -
Marie Magna n fo r th e beautifu l poste r tha t sh e dre w fo r th e conference . Th e
hospitality extende d b y Howar d Universit y wa s exemplary , an d helpe d t o creat e a
serene atmosphere ideally suited for a research conference. I would also like to than k
all th e speaker s wh o gav e additiona l lecture s a t th e conference . Th e paper s base d
on thei r beautifu l presentations , whic h hav e just bee n publishe d b y th e America n
Mathematical Societ y a s Volum e 28 5 o f th e Contemporar y Mathematic s Series ,
contain furthe r development s t o man y o f th e theme s an d question s allude d t o i n
my lectures . The y provid e a n excellen t complemen t t o thi s monograph .
I woul d lik e t o than k th e Nationa l Scienc e Foundatio n fo r havin g funde d thi s
research conferenc e throug h th e Conferenc e Boar d o f th e Mathematica l Sciences ,
and th e Natura l Science s an d Engineerin g Researc h Counci l o f Canad a fo r havin g
funded m y researc h continuousl y sinc e 1986.
I woul d lik e t o than k th e colleague s an d friend s wh o gav e m e their encourage -
ments durin g th e preparatio n o f my lectures , i n particula r Henr i Darmon , Feli x
xii i
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