Pavel Etingof, MIT
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Forms of tensor categories over arbitrary fields.
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Abstract: I will explain how to classify forms of a tensor category over a
not necessarily algebraically closed field, and give explicit
examples of classification of such forms. I will also discuss the problem of
categorification of weak fusion rings, and classify
categorifications for the simplest families of such rings. This leads to
interesting questions in both elementary and
advanced number theory, such as the classification of regular polygons
constuctible by compass and ruler (i.e., Fermat
primes), the Merkurjev-Suslin theorem, and global class field theory. The
talk is based on joint work with Shlomo Gelaki.