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

News

- See my slides from Algorithmic Randomness Interacts with Analysis and Ergodic Theory: [slides] [video]
- See my slides from a special session of the AMS Central Sectional 2016: [slides]
- 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 mathematician 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.

*Currently Teaching:*

Math 457: Introduction to Mathematical Logic (Spring 2017).

Math 230: Calculus and Vector Analysis (Spring 2017).

*Past Teaching:*

Math 141: Calculus with Analytic Geometry II (Fall 2016).

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

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).

Schnorr randomness for noncomputable measures

Submitted.
[arXiv]

Algorithmic randomness and Fourier analysis

with Johanna N.Y. Franklin,
Timothy H. McNicholl

Submitted.
[arXiv]

Energy randomness

with Joseph S. Miller.

*Israel Journal of Mathematics*.
Accepted.
[arXiv]

When does randomness come from randomness?

*Theoretical Computer Science*.
Accepted. Available online.
[arXiv]
[doi]

A formal proof of the Kepler conjecture

with Thomas Hales
and 20 others.

Submitted.
[arXiv]
(This is part of the "Flyspeck project." I played a small role formally verifying some geometry facts.)

Algorithmic randomness, martingales and differentiation

[preprint]

Computable randomness and betting for
computable probability spaces

*Mathematical Logic Quarterly*.
62(4–5):335–366, 2016.
[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

Algorithmic randomness and maps with computable conditional probability

[abstract]

On the computability of rates of metastable convergence

[abstract]

Algorithmic randomness for capacities with applications to random closed sets

[abstract]

Algorithmic randomness and computable measure theory

[abstract]

Algorithmic randomness for locally finite measures

[abstract]

Schnorr randomness for noncomputable measures

Algorithmic Randomness Interacts with Analysis and Ergodic Theory,
December 5–9, 2016

[slides]
[video]

A uniform reducibility in computably presented Polish spaces

Effective Mathematics in Discrete and Continuous Worlds
(AMS Sectional), October 28–30, 2016

[abstract]
[slides]

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".