Patrick Lutz

Most of my research is in computability theory and descriptive set theory (and their intersection, effective descriptive set theory). One of the main focuses of my work in computability theory is Martin's Conjecture, a long-standing open question which concerns the special role of the halting problem in computability theory. I have also worked on various other topics in computability theory, including algorithmic randomness and computable model theory. In descriptive set theory, I have mainly worked on the theory of Borel and analytic equivalence relations. I am also interested in mathematical logic much more generally and I am interested in any questions in logic which are philosophically well-motivated and contain substantial mathematical content. In the past I have dabbled in topics like the failures of the Axiom of Choice and formal verification of mathematics.