Betti numbers of modules over Noetherian rings with ... - IPM

Acknowledgments
I would like to thank Professor Siamak Yassemi, my supervisor, for his many
suggestions and constant support during this research. I am also thankful to Professor
Rahim Zaare-Nahandi for his encouragement, advice and mindful hints.
I had the pleasure of meeting Professor Aldo Conca in the Mathematics Depart-
ment of University of Genova-Italia. I am indebted to him for many helpful discussions
during Sep. 2007- Apr. 2008. I would like to express my deep gratitude to him for
generosity with his ideas, invaluable time, and kind hospitality.
I was fortunate to meet Professor Jürgen Herzog in Universität Duisburg-Essen
and giving a talk on graded Betti numbers and behavior of Castelnuovo-Mumford
regularity. I would like to thank him for the kind invitation and special attention.
Further, I wish to acknowledge the contribution of Professors Graham Leuschke,
Amelia Taylor, Yuji Yoshino, Brian Harbourne, Juan Migliore and Hans Schoutens
for helpful suggestions that went into the material of this thesis. My heartfelt thanks
goes to Professor Sean Sather-Wagstaff and Professor Giuseppe Valla for fruitful
discussions in several personal communications. I gratefully acknowledge the role
of Computer Algebra systems CoCoA and Macaulay 2 in computations of concrete
examples as we worked on the project.
The Mathematics Department of University of Genova (DIMA), the Ministry of
Science, Research and Technology of Islamic Republic of Iran and the Institute for
Theoretical Studies in Physics and Mathematics (IPM) also have my sincere thanks
for the partial support and providing the facilities for some part of my research.
Of course, I am grateful to my parents and my wife for their patience and love.
Without them this work would never have come into existence (literally).
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