Two central problems in computer science are P vs NP and the
complexity of matrix multiplication. The first is also a leading
candidate for the greatest unsolved problem in mathematics. The
second is of enormous practical and theoretical importance.
Algebraic geometry and representation theory provide fertile ground
for advancing work on these problems and others in complexity. This
introduction to algebraic complexity theory for graduate students
and researchers in computer science and mathematics features
concrete examples that demonstrate the application of geometric
techniques to real world problems. Written by a noted expert in the
field, it offers numerous open questions to motivate future
research. Complexity theory has rejuvenated classical geometric
questions and brought different areas of mathematics together in
new ways. This book will show the beautiful, interesting, and
important questions that have arisen as a result.
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