|Department of Mathematical
Carnegie Mellon University
Pittsburgh, PA 15213
Office: Wean Hall 7106
My research is in mathematical logic—proof theory and computability
theory. My interests are best summed up by this quotation
Miller's research statement:
To this aim, I am working on problems in algorithmic randomness, reverse mathematics, proof mining, metastability, and effective mathematics (especially related to measure theory, probability theory, and ergodic theory).
Computable randomness and betting for
computable probability spaces
Algorithmic randomness, martingales, and differentiation I
This paper examines the Lebesgue Differentiation Theorem, the Levy 0-1 Law, and other martingale and differentiability theorems using computable analysis and algorithmic randomness. It focuses on Schnorr randomness and effective convergence. [prelim draft]
Algorithmic randomness, martingales, and differentiation II
This paper examines martingale convergence and differentiability using computable analysis and algorithmic randomness. It focuses on computable randomness, Martin-Lof randomness, and non-effective convergence.
Transformations which preserve computable randomness
This paper extends the results of Computable randomness and betting for computable probability spaces (see above) to show that computable randomness is preserved by Schnorr-layerwise-computable isomorphisms and certain Schnorr-layerwise-computable morphisms.
(upcoming) Algorithmic randomness for Doob's martingale
convergence theorem in continuous time
Computability complexity and analysis, July 8-10, 2013
(upcoming) Schnorr randomness for noncomputable measures
Computability in Europe, July 1-5, 2013
(upcoming) Transformations which preserve computable randomness
Algorithmic Randomness and Analysis, June 27-28, 2013
Ultrafilters and Ergodic Theory
Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory,
October 7-19, 2012
randomness and its properties
7th Conference on Computability, Complexity and Randomness, July 2-6, 2012.
[slides] [abstract & video (35 min)]
I used to maintain an unofficial graduate student homepage directory.
Sometimes Google auto-corrects my name to "Jason Route".