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

Math 557: Mathematical Logic (Graduate) (Fall 2015).

Math 231: Calculus of Several Variables (Fall 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

When does randomness come from randomness?
[arXiv]

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
New England Definability and Recursion Seminar, October 17, 2015

(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".