Karthik
Ravishankar.

I’m a fifth-year PhD student in mathematics at the University of Wisconsin–Madison, working with Joseph Miller in computability theory. Computability is a branch of mathematical logic that studies the limits of algorithms and Turing machines. By classifying problems according to their relative degrees of unsolvability, we obtain the rich structure of the Turing degrees, which calibrates computational strength.

I’m interested in local and global questions about the Turing and enumeration degrees. One current project characterizes levels of genericity through notions of computational strength. In computable structure theory, I’m studying degree spectra within the Δ⁰₂ degrees, as well as unions of spectra. Another project examines the information encodable in two jumps of a linear order.

I work in Lean and am interested in formalizing mathematics.

In past work on Ahmad pairs, I showed that the left half must be low₃ and the right half high₂. This separated the two halves and led to natural Π₃ definitions of low₃ and high₂ in the local structure.