12:00
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Starting from the principle of locality in quantum field theory, which
states that an object is influenced directly only by its immediate
surroundings, I will first briefly review some features of the notion of
locality arising in physics and mathematics. These are then encoded
in locality relations, given by symmetric binary relations whose graph
consists of pairs of "mutually independent elements".
I will mention challenging questions that arise from enhancing algebraic
structures to their locality counterparts, such as i) when is the quotient
of a locality vector space by a linear subspace, a locality vector space, if
equipped with the quotient locality relation, ii) when does the locality
tensor product of two locality vector spaces define a locality vector
space. These are discussed in recent joint work with Pierre Clavier, Loïc
Foissy and Diego López.
Locality morphisms, namely maps that factorise on products of pairs of
"mutually independent" elements, play a key role in the context of
renormalisation in
multiple variables. They include "locality evaluators", which we use to
consistently evaluate meromorphic germs in several variables at
their poles. I will also report on recent joint work with Li Guo and Bin
Zhang. which gives a classification of locality evaluators on certain
classes of algebras of meromorphic germs.