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

News

- I will attend the Joint Math Meetings in January 2016.
- See my slides from NERDS Fall 2015: [slides]
- See my slides from Computability Theory and Applications (AMS Sectional): [slides]
- See my slides from CIE 2015: [slides]
- See my slides from CCR 2015: [slides]
- See my slides from VAI 2015: [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.

Math 457: Introduction to Mathematical Logic (Spring 2016).

*Past Teaching:*

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

Math 231: Calculus of Several Variables (Fall 2015).

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).

Energy randomness

with Joseph S. Miller.

In preparation.
[arXiv]

When does randomness come from randomness?

Submitted.
[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.
[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]

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

Computing uniform (metastable) rates of convergence from the statement of the theorem alone

New England Recursion and Definability Seminar (NERDS),
October 17, 2015

[abstract]
[slides]

An application of computable continuous model theory to a question in proof theory

AMS Sectional Meeting:
Computability Theory and Applications, October 3–4, 2015

[abstract]
[slides]

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]

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