This volume contains original research and survey papers stemming from the AMS-
IMS-SIAM Joint Summer Research Conference "Integer points in Polyhedra- Ge-
ometry, Number Theory, Representation Theory, Algebra, Optimization, Statis-
tics.", which took place from June 11 to June 15, 2006, in Snowbird, Utah. The con-
ference website
/math. sf su. edu/beck/ src06. html
contains the program
and pictures of the conference.
The volume is a cross section of recent advances connected to lattice-point ques-
tions. Similar to the talks given at the conference, topics range from commutative
algebra to optimization, from discrete geometry to statistics, from mirror symmetry
to geometry of numbers.
We thank the AMS, IMS, and SIAM for their generous support, which allowed
us, among other things, to sponsor undergraduate and graduate students for the
conference. We would like to express our deep gratitude to Wayne Drady, the
local AMS organizer in Snowbird, who made sure--once more in his most pleasant
way-that our conference ran smoothly in every possible aspect.
We are grateful to all contributors and the anonymous referees for invaluable
help. Many thanks to Christine Thivierge and her staff for their patience and for
their assistance in preparing these proceedings.
Finally, thanks to all participants of the conference, for making it such a pleas-
ant and productive event.
Matthias Beck
Christian Haase
Bruce Reznick
Michele Vergne
Volkmar Welker
Ruriko Yoshida
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