Department of Mathematics Pennsylvania State University State College, PA 16802 Email: Office: 421 McAllister Bldg |

News

- I am an invited speaker at Computability, Complexity and Randomness, June 2015
- I am an invited speaker at the Southeastern Logic Symposium (SEALS), March 2015
- See my slides from CCR 2014: [slides]

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.

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).

Algorithmic randomness, martingales and differentiation

[preprint]

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]

Oscillation and the mean ergodic theorem for uniformly
convex Banach spaces

with Jeremy Avigad.

*Ergodic Theory and Dynamical Systems*.
Published Online 2014.
[arXiv]
[doi]

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]

Computable randomness and betting for
computable probability spaces

Submitted.
[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]

*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

Randomness for capacities with applications to random closed sets.

Computability, Complexity and Randomness (CCR), June, 2014

[abstract]
[slides]

Computable randomness and martingales a la probability theory.

UConn Logic Seminar, November 13, 2012

[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]

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