He gave his talk on Wednesday May 20th. Afterwards we discussed it on the Category Theory Community Server, here:
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• Gordon Plotkin, A complete axiomatisation of partial differentiation.
Abstract. We formalise the well-known rules of partial differentiation in a version of equational logic with function variables and binding constructs. We prove the resulting theory is complete with respect to polynomial interpretations. The proof makes use of Severi’s theorem that all multivariate Hermite problems are solvable. We also hope to present a number of related results, such as decidability and Hilbert–Post completeness.