Acknowledgements
Tight closur e bega n i n a conversatio n wit h Me l Hochste r a t a conferenc e a t
the Universit y o f Illinois in November o f 1986. Seriou s work on tight closur e bega n
early i n 1987, and th e subjec t quickl y too k flight . Withou t Me l Hochster th e topi c
of thi s manuscrip t woul d no t exist , an d thes e note s ar e a tribut e t o hi s beautifu l
ideas an d immens e contributions .
Many othe r peopl e hav e helpe d m e i n bot h m y thinkin g an d writing . I ow e
special thanks t o Ian Aberbach , Bil l Heinzer, Jo e Lipman, Kare n Smith , an d Iren a
Swanson. I thank Jane t Cowde n fo r proofreadin g th e entir e manuscript .
These note s ar e base d o n te n talk s I gav e a t a CBM S conferenc e a t Nort h
Dakota Stat e Universit y Jun e 22-29 , 1995. A special thank s goe s to th e organizer ,
Joe Brennan . I a m ver y gratefu l t o hi m fo r th e ide a o f havin g thi s conference ,
and fo r th e tim e an d effor t h e pu t int o i t t o mak e i t a success . Hi s effort s mad e
the conferenc e bot h pleasan t an d enjoyable . I als o than k Nort h Dakot a Stat e
University fo r hostin g th e conference , th e Conferenc e Boar d o f th e Mathematica l
Sciences fo r choosin g thi s topic , an d th e Nationa l Scienc e Foundatio n fo r fundin g
it. I woul d lik e t o than k th e mai n supportin g speakers : Ia n Aberbach , Juerge n
Herzog, Me l Hochster , Jo e Lipman , Pau l Monsky , Pau l Roberts , Kare n Smith ,
Mark Spivakovsky , an d Kei-ich i Watanabe . Thei r talk s enhance d th e conferenc e
greatly.
Finally, I thank th e University of Michigan for support durin g my preparation s
for th e conference .
Craig Huneke , August , 1995
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