Jason Rute

Jason Rute - Nov 24, 2009

     [About Me]      [Teaching]      [Publications]      [Dissertation]      [Recent Talks]      [Other]

News

About Me

I am a research associate (post doc) at Penn State specializing in mathematical logic.

In 2013, I received my Ph.D. in Mathematical Science from Carnegie Mellon University under Jeremy Avigad.

I am interested in the nontrivial interactions between computable mathematical structure and classical mathematical structure. To this aim, I work on problems in algorithmic randomness, reverse mathematics, effective mathematics, and quantitative analysis (including metastability).

See my Curriculum Vitae and Research Statement for more information.

Teaching

I am not teaching Spring 2015.

Past Teaching:

Math 558: Foundations of Mathematics (Graduate) (Fall 2014).

Math 230: Calculus and Vector Analysis (Fall 2014).

Math 457: Introduction to Mathematical Logic (Spring 2014).

Math 230: Calculus and Vector Analysis (Fall 2013).

Publications

Algorithmic randomness, martingales and differentiation
[preprint]

Computable randomness and betting for computable probability spaces
To appear in Mathematical Logic Quarterly. [arXiv]

Oscillation and the mean ergodic theorem for uniformly convex Banach spaces
with Jeremy Avigad.
Ergodic Theory and Dynamical Systems. 34(5):1009–1027, 2015. [arXiv] [doi]

Algorithmic randomness for Doob’s martingale convergence theorem in continuous time
with Paul K. L. Nguyen, Bjørn Kjos-Hanssen.
Logical Methods in Computer Science. 10(4:12):1–35, 2014. [link]

Van Lambalgen's theorem for uniformly relative Schnorr and computable randomness
with Kenshi Miyabe.
Proceedings of the 12th Asian Logic Conference, 251–270, 2013. [arXiv] [doi]

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]

Dissertation

Topics in algorithmic randomness and computable analysis
PhD dissertation. Carnegie Mellon University, 2013. [link]
Consists of the following two papers:
     Computable randomness and betting for computable probability spaces
     Algorithmic randomness, martingales and differentiation

Recent Talks

(Upcoming) TBA
AMS Sectional Meeting: Computability Theory and Applications, October 3–4, 2015

Randomness for ergodic measures
Computability in Europe, June 29–July 3, 2015
[slides]

New directions in randomness
Computability, Complexity, and Randomness, June 22–26, 2015
[slides]

Algorithmic randomness and constructive/computable mathematics
Varieties of Algorithmic Information, June 15–18, 2015
[slides]

Randomness, Brownian motion, Riesz capacity, and complexity
Southeastern Logic Symposium (SEALS), February, 2015
[abstract] [slides]

Randomness for capacities with applications to random closed sets
Computability, Complexity and Randomness (CCR), June, 2014
[abstract] [slides]

The power of uniformity in algorithmic randomness
UConn Logic Seminar, March 10, 2014
[abstract] [handout]

Schnorr randomness for noncomputable measures
Joint Mathematics Meeting: Special Session on Logic and Probability, January 15–18, 2014
[abstract] [slides]

Schnorr randomness and computable analysis
AMS Sectional Meeting: Computability Across Mathematics, October 19–20, 2013
[slides]

Topics in algorithmic randomness and computable analysis (PhD defense presentation)
Carnegie Mellon University, Mathematical Sciences Dept, August 8, 2013
[slides]

Algorithmic randomness for Doob's martingale convergence theorem in continuous time
Computability and complexity in analysis, July 8–10, 2013
[slides]

Schnorr randomness for noncomputable measures
Computability in Europe, July 1–5, 2013
[slides]

Transformations which preserve computable randomness
Algorithmic Randomness and Analysis, June 27–28, 2013
[abstract] [slides]

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

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