"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

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

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

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

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