On June 29, 2022 at 16:00 EEST, Nicholas Pischke (Technische Universität Darmstadt) will give a talk in the Proof Mining Seminar.
Title: Proof mining for maximally monotone set-valued operators
Abstract: I discuss how proofs involving set-valued operators and their resolvents can be treated in higher-type arithmetic while attaining logical bound extraction theorems. In particular, I focus on a specific class of so-called “maximally monotone” operators which are ubiquitous in the literature. In that context, I discuss how one can circumvent the logically complicated maximality statement by utilizing Minty’s theorem, a fundamental result from monotone operator theory, and still obtain mathematically strong systems which allow for the explanation of most of the previous case studies involving said operators. This leads to a surprising and robust connection between the maximality statement and formal extensionality of the operator which I discuss in conjunction with various quantitative forms of (fragments of) the extensionality (viz. maximality) statement which can still be used in the context of the previously mentioned bound extraction theorems.
Google Meet link: https://meet.google.com/xwm-syvx-bbr