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This book focusses on a large class of objects in moduli theory and
provides different perspectives from which compactifications of
moduli spaces may be investigated. Three contributions give an
insight on particular aspects of moduli problems. In the first of
them, various ways to construct and compactify moduli spaces are
presented. In the second, some questions on the boundary of moduli
spaces of surfaces are addressed. Finally, the theory of stable
quotients is explained, which yields meaningful compactifications
of moduli spaces of maps. Both advanced graduate students and
researchers in algebraic geometry will find this book a valuable
read.
This book provides a largely self-contained and broadly accessible
exposition on two cosmological applications of algebraic quantum
field theory (QFT) in curved spacetime: a fundamental analysis of
the cosmological evolution according to the Standard Model of
Cosmology; and a fundamental study of the perturbations in
inflation. The two central sections of the book dealing with these
applications are preceded by sections providing a pedagogical
introduction to the subject. Introductory material on the
construction of linear QFTs on general curved spacetimes with and
without gauge symmetry in the algebraic approach, physically
meaningful quantum states on general curved spacetimes, and the
backreaction of quantum fields in curved spacetimes via the
semiclassical Einstein equation is also given. The reader should
have a basic understanding of General Relativity and QFT on
Minkowski spacetime, but no background in QFT on curved spacetimes
or the algebraic approach to QFT is required.>
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