Preface

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

http:

I

/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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