Title: Petri nets and processes

Abstract: Petri nets are a very useful formalism for modelling processes,
with applications in many different fields of science and engineering such
as chemistry, epidemiology, computer science, and business and production
modelling. Their operational semantics come in two main flavours: geometric
(in terms of posets, graphs, and such), and algebraic (in terms of monoids,
monoidal categories, etc.). People have struggled for many years to
reconcile the two viewpoints, the problem being an issue with symmetries.
In this talk I will explain how the problem can be overcome with the help
of some elementary homotopy viewpoints. The new formalism for Petri nets is
based on polynomial-style finite-set configurations and etale maps. The
processes of a Petri net P are etale maps G -> P from graphs. The main
result I want to arrive at is that P-processes (the geometric semantics)
form a symmetric monoidal Segal space, and that this is the free
prop-in-groupoids on P (thus at the same time the algebraic semantics). 
But most of the time will be spent just explaining Petri nets, markings,
firings, and the token game.

Reference: "Elements of Petri nets and processes" [ArXiv:2005.05108]