24 June 2017:

1) Daniel Cicala submitted an abstract for my AMS special session on Applied Category Theory:

* A bicategorical syntax for pure state qubit quantum mechanics

> **Abstract.** We begin by constructing a framework used to study open networks modeled by graphs and their rewritings. This consists of a symmetric monoidal compact closed bicategory built by combining spans and cospans inside a topos. Into this bicategorical framework, we fit Coecke and Duncan’s zx-calculus, a graphical language used to reason about pure state qubit quantum mechanics. After viewing the zx-calculus through this lens, we highlight several benefits over the 1-categorical approach: the presence of a symmetric monoidal compact closed structure and a better representation of rewriting information. (Received June 22, 2017)

2) So did Brendan Fong:

* Black boxes and decorated corelations

> **Abstract.** Consider an electric circuit. Suppose this circuit has chosen terminals, which we may connect with the terminals of another circuit. That is to say, consider that we may compose two circuits to obtain another circuit. This suggests we might model circuits as morphisms in a category. Next, suppose I want to compose a circuit with a resistor of resistance 2 ohms. If I have no such resistors, I could substitute with a pair of 1 ohm resistors in series. This suggests a coarser representation of circuits, one that keeps track of only how the circuit behaves, and not their [its] constituent components. In this talk I shall introduce decorated corelations as a tool for constructing categories that model circuits, and constructing ‘black box’ functors that shift between these models. This framework is applicable not only to circuits, but to open systems in general. (Received June 23, 2017)