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"Ideas from quantum field theory and string theory have had an enormous impact on geometry over the last two decades. One extremely fruitful source of new mathe
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This is the first volume of the lectures presented at the Clay Mathematics Institute 2014 Summer School, ``Periods and Motives: Feynman amplitudes in the 21st c
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The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces whe
Mixed Hodge Structures and Singularities
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This vital work is both an introduction to, and a survey of singularity theory, in particular, studying singularities by means of differential forms. Here, some
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In recent years, the old idea that gauge theories and string theories are equivalent has been implemented and developed in various ways, and there are by now va