LSV Seminar

Date

26.11.2019, 11:00

Place

Pavillon des Jardins

Speaker

Nicolas Behr (IRIF)

While the theory of rewriting over adhesive categories enjoys a rich history within (at least a niche of) the computer science community with over 40 years of developments, rewriting is a concept comparatively little known within the applied sciences and even general mathematics communities. In this talk, I will present a number of recent developments that permit to overcome this conceptual divide, first and foremost in the form of so-called rule algebras. The latter encode the non-determinism in sequential compositions of rewriting steps in a form reminiscent of the theory of the so-called Heisenberg-Weyl algebra. The Heisenberg-Weyl algebra in turn encodes the combinatorics of the formal operations of multiplication with and derivation by the formal variable considered as linear operators on the vector space of formal power series. The construction of rule algebras is based upon a previously unknown property of (a form of) associativity of sequential rule compositions, the proof of which intimately relies upon the framework of adhesive categories. Together with a number of additional constructions motivated from mathematical physics, I will present a number of applications of the rule algebra formalism from the fields of chemistry, biochemistry, social sciences and combinatorics for illustration. In particular, since the core of the rule algebra formalism is given by adhesive category theory in its various incarnations, applications of rewriting theory to the aforementioned fields are considerably facilitated via having available a universal framework for formulating mathematical concepts such as stochastic mechanics (CTMCs) and generating function evolution equations. I will conclude with an outlook on work in progress, with a focus on further perspectives of this approach in the field of applied category theory.