This is a selection of my talk slides, presented in reverse chronological order. Together they summarize my contributions to various areas of computability theory.
- Computabiilty of K-theory of operator algebras. This talk discusses recent work by myself, Chris Eagle, Isaac Goldbring, and Russell Miller on computing the K_0 group of a computably presented C* algebra along with some applications to AF and UHF algebras.
- Computability theory of operator algebras. This talk summarizes recent work by myself and a number of other people on the computability of the Gelfand transform functor. It was delivered at the AMS Spring Central Sectional Meeting at University of Milwaukee in 2024.
- Computable presentations of metric structures. My attempt to summarize everything known at the time about effective metric structure theory along with some open problems. It was given at the 2023 meeting of Computability and Complexity in Analysis in Kochel am See in Germany.
- Presentations and theories of metric structures A discussion of work by myself and others on the complexity of presentations of metric structures and theories of metric structures (in the sense of continuous logic). Delivered at the 2022 Southeastern Logic Symposium at the University of Florida.
- An application of computable probability to computable analysis. The title disguises it, but this is actually a discussion of the problem of computing p from a presentation of an L^p space (of dimension > 1). This leads into a tour of some old-school probability and functional analysis. Given at the Spring 2020 meeting of the Iowa Colloquium on Information and Complexity in Logic (ICICL).
- Index sets of classes of Lebesgue spaces Summarizes my work with Sasha Melnikov and Tyler Brown on various classification problems related to L^p spaces. The isometric isomorphism problem turned out to belong to an unusual complexity classes. Delivered at the 2019 Asian Logic Conference in Astana, Kazakhstan.
- Isometry degrees of computable copies of l^p These are the minimal Turing degrees that compute an isometric isomorphism from a computable presentation of l^p to the standard presentation. It was joint work with Don Stull. To our surprise, these turned out to be the c.e. degrees. Presented at the 2016 Southeastern Logic Symposium.
- Making meaning in large lectures via clickers Actually a math-ed. talk; essentially my only one. Given to the mathematical education seminar at Arizona State University.
- Interactions between computability and complex analysis My last talk on computable complex analysis (probably), and arguably my first on effective metric structure theory (in particular, computability of Banach spaces). The focus is on Hardy spaces. Given at the Fall 2014 meeting of the Midwestern Computability Seminar at the University of Chicago.
- An exploration of effective local connectivity. A mixture of computable topology and computable complex analysis. It was one of the invited talks at the 2014 Computability and Complexity in Analysis meeting at TU-Darmstadt.
- How to hide from a nanobot I discussed points in the plane that avoid certain classes of computable curves. Delivered during a special session at the 2012 Joint Mathematics Meetings. The title led to a very full room!
- A potential-theoretic construction of the Schwarz-Christoffel map for multiply connected domains Not a computability talk, but the results, which are pure complex analysis, were inspired by questions in computable complex analysis. Joint work with Valentin Andreev. Delivered at a special session during the Fall 2011 Central Sectional Meeting of the American Mathematical Society.
- Blaschke products and inner functions from the viewpoint of the theory of computation One of my early talks on computable complex analysis. It was an invited talk to a meeting on Blaschke products at the Fields Institute in 2011.