Jason Rute

Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213 Email:   Office: Wean Hall 7106

I have been a Ph.D student in the Pure and Applied Logic program at Carnegie Mellon University since Fall 2008. My advisor is Jeremy Avigad.

My research is in mathematical logic—proof theory and computability theory.  My interests are best summed up by this quotation from Joe 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).

See my Curriculum Vitae and Research Statement for more information.

Publications

Van Lambalgen's theorem for uniformly relative Schnorr and computable randomness
with Kenshi Miyabe.
Accepted to Proceedings of the 12th Asian Logic Colloquium. [arXiv]

Computable randomness and betting for computable probability spaces
Submitted. [arXiv]

Oscillation and the mean ergodic theorem for uniformly convex Banach spaces
with Jeremy Avigad.
[arXiv]

Algorithmic randomness, reverse mathematics, and the dominated convergence theorem
with Jeremy Avigad, Edward Dean.
Annals of Pure and Applied Logic, 163(12):1854-1864, 2012. [arXiv] [doi]

A metastable dominated convergence theorem
with Jeremy Avigad, Edward Dean.
Journal of Logic and Analysis, 4:3:1-19, 2012. [doi]

Papers In Preparation

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.

Recent Talks

The computability of martingale convergence
Joint Mathematics Meeting / ASL Contributed Paper Session, January 9-12, 2013
[abstract] [slides]

Computable randomness and martingales a la probability theory
Penn State Logic Seminar, November 13, 2012
[abstract] [slides]

Ultrafilters and Ergodic Theory
Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory,
October 7-19, 2012
[extended abstract]

Martingale convergence and algorithmic randomness
Logic Colloquium 2012, July 12-18, 2012.
[slides]

Computable randomness and its properties
7th Conference on Computability, Complexity and Randomness, July 2-6, 2012.
[slides] [abstract & video (35 min)]

Computable randomness for computable probability spaces
Twelfth Asian Logic Conference (Invited speaker), December 15-20, 2011.
[slides]

Randomness, martingales and differentiability
Randomness and Analysis in Auckland, December 12-13, 2011.
[abstract] [slides]

Randomness and the Lebesgue Differentiation Theorem
Southern Wisconsin Logic Colloquium, May 10, 2011.
[slides]

Randomness and the Lebesgue Differentiation Theorem
Graduate Student Conference in Logic, May 7, 2011.
[slides]

Other

I used to maintain an unofficial graduate student homepage directory.

Sometimes Google auto-corrects my name to "Jason Route".