viii PREFACE
This is but a brief snapshot of intersections, so we invite the reader to peruse the
abstracts for a better summary of the papers.
Of course, the true mathematical objects underlying polynomial system
solving are simultaneously arithmetic and geometric. The more arithmetically
or geometrically inclined reader will thus also find much on which to meditate:
A-discriminants, flat families, fewnomial theory (over R, Qp, and other fields),
amoeba theory, coamoeba theory, tropical varieties, mixed volume, sums of squares,
monodromy from a computational point of view, and determinantal representations
of the permanent.
We hope the reader will catch a glimpse here of the remarkable depth, breadth,
and beauty of algorithmic algebraic geometry.
We gratefully acknowledge the support of the the Banff International Research
Station, the Department of Energy (ASCR grant DE-SC0002505), the National
Science Foundation (MCS grant DMS-0915245), and Sandia National
Laboratories.1
The Editors:
Leonid Gurvits
Philippe P´ebay
J. Maurice Rojas
David Thompson
July 11, 2011
1Sandia
is a multiprogram laboratory operated and managed by Sandia Corp., a Lockheed
Martin Company, for the US Dept. of Energy under contract DE-AC04-94AL85000.
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