Publications

Books

1. Effective Metric Structure Theory (with Isaac Goldbring and Timothy H. McNicholl). Springer, Monographs in Mathematics, 2026.
   
   
2. Revolutions and Revelations in Computability (co-edited with Ulrich Berger, Florin Manea, and Arno Pauly). Springer, Lecture Notes in Computer Science, vol. 13359, 2022.
   
   
3. Algorithmic Randomness: Progress and Prospects (co-edited with Christopher P. Porter). Cambridge University Press, Lecture Notes in Logic, vol. 50, 2020.
   
   

Published/Accepted articles

1. Free structures and limiting density (with Julia F. Knight and Meng-Che Ho) (arXiv)
   Fundamenta Mathematicae, vol. 274, pp. 119-174, 2026.
   
   
2. Failure modes for structural highness notions (with Wesley Calvert and Dan Turetsky) (arXiv)
   Journal of Logic and Computation, vol. 35(7), exaf051, 2025.
   
   
3. Represented spaces of represented spaces (with Eike Neumann, Arno Pauly, Cécilia Pradic, and Manlio Valenti)
   In Beckmann, Arnold and Oitavem, Isabel and Manea, Florin, eds., Lecture Notes in Computer Science, vol. 15764, pp. 47-61, 2025.
   
   
4. Computable classifications of continuous, transducer, and regular functions (with Rupert Hölzl, Alexander Melnikov, Keng Meng Ng, and Daniel Turetsky) (arXiv)
   Theoretical Computer Science, vol. 1032, Paper No. 115086, 2025.
   
   
5. Structural highness notions (with Wesley Calvert and Dan Turetsky) (arXiv)
   Journal of Symbolic Logic, vol. 88(4), pp. 1692-1724, 2023.
   
   
6. A Church-Turing Thesis for Randomness? (.pdf, typo on second page corrected from published version)
   In L. De Mol, A. Weiermann, F. Manea, and D. Fernández-Duque, eds., Lecture Notes in Computer Science, vol. 12813, pp. 217-226, 2021.
   
   
7. Degrees of and lowness for isometric isomorphism (with Timothy H. McNicholl) (arXiv)
   Journal of Logic and Analysis, vol. 12(6), pp. 1-23, 2020.
   
   
8. Key developments in algorithmic randomness (survey paper with Christopher P. Porter).
   In J. Franklin and C. Porter, eds., Algorithmic Randomness: Progress and Prospects, pp. 1-39. Cambridge University Press, 2020.
   
   
9. Relativization in randomness (survey paper).
   In J. Franklin and C. Porter, eds., Algorithmic Randomness: Progress and Prospects, pp. 134-174. Cambridge University Press, 2020.
   
   
10. Lowness for isomorphism, countable ideals, and computable traceability (with Reed Solomon) (arXiv)
    Mathematical Logic Quarterly, vol. 66(1), pp. 104-114, 2020.
    
    
11. Taking the path computably traveled (with Dan Turetsky) (arXiv)
    Journal of Logic and Computation, vol. 29(6), pp. 969-973, 2019.
    
    
12. Algorithmic randomness and Fourier analysis (with Timothy H. McNicholl and Jason Rute) (arXiv)
    Theory of Computing Systems, vol. 63(3), pp. 567-586, 2019.
    
    
13. Lowness for isomorphism and degrees of genericity (with Dan Turetsky) (.pdf)
    Computability, vol. 7(1), pp. 1-6, 2018.
    
    
14. Strength and weakness in computable structure theory (survey paper) (.pdf)
    In A. Day et al., eds., Lecture Notes in Computer Science, vol. 10010, pp. 302-323, 2017.
    
    
15. Genericity and UD-random reals (with Wesley Calvert) (.pdf)
    Journal of Logic and Analysis, vol. 7(4), pp. 1-10, 2015.
    
    
16. Randomness and nonergodic systems (with Henry Towsner) (.pdf)
    Moscow Mathematical Journal, vol. 14, pp. 711-744, 2014.
    
    
17. Degrees that are low for isomorphism (with Reed Solomon) (.pdf)
    Computability, vol. 3, pp. 73-89, 2014.
    
    
18. omega-change randomness and weak Demuth randomness (with Keng Meng Ng) (.pdf)
    Journal of Symbolic Logic, vol. 79, pp. 776-791, 2014.
    
    
19. Lowness for difference tests (with David Diamondstone) (.pdf)
    Notre Dame Journal of Formal Logic, vol. 55, pp. 63-73, 2014.
    
    
20. Anti-complex sets and reducibilities with tiny use (with Noam Greenberg, Frank Stephan, and Guohua Wu) (.pdf)
    Journal of Symbolic Logic, vol. 78, pp. 1307-1327, 2013.
    
    
21. Local computability for ordinals (with Asher M. Kach, Russell Miller, and Reed Solomon) (.pdf)
    In P. Bonizzoni, V. Brattka, and B. Loewe, eds., Lecture Notes in Computer Science, vol. 7921, pp. 161-170, 2013.
    
    
22. Degrees of categoricity and the hyperarithmetic hierarchy (with Barbara F. Csima and Richard A. Shore) (.pdf)
    Notre Dame Journal of Formal Logic, vol. 54, pp. 215-231, 2013.
    
    
23. Martin-Loef random points satisfy Birkhoff's ergodic theorem for effectively closed sets (with Noam Greenberg, Joseph S. Miller, and Keng Meng Ng) (.pdf)
    Proceedings of the AMS, vol. 140, pp. 3623-3628, 2012.
    
    
24. Relativizations of randomness and genericity notions (with Frank Stephan and Liang Yu) (.pdf)
    Bulletin of the London Mathematical Society, vol. 43, pp. 721-733, 2011.
    
    
25. Van Lambalgen's Theorem and high degrees (with Frank Stephan) (.pdf)
    Notre Dame Journal of Formal Logic, vol. 52, pp. 173-185, 2011.
    
    
26. A superhigh diamond in the c.e. tt-degrees (with Douglas Cenzer, Jiang Liu, and Guohua Wu) (.pdf)
    Archive for Mathematical Logic, vol. 50, pp. 33-44, 2011.
    
    
27. Difference randomness (with Keng Meng Ng) (.pdf)
    Proceedings of the AMS, vol. 139, pp. 345-360, 2011.
    
    
28. Subclasses of the weakly random reals (.pdf)
    Notre Dame Journal of Formal Logic, vol. 51, pp. 417-426, 2010.
    
    
29. Schnorr trivial sets and truth-table reducibility (with Frank Stephan) (.pdf)
    Journal of Symbolic Logic, vol. 75, pp. 501-521, 2010.
    An earlier version was published as Technical Report TRA3/08, School of Computing, National University of Singapore, 2008.
    
    
30. Schnorr triviality and genericity (.pdf)
    Journal of Symbolic Logic, vol. 75, pp. 191-207, 2010.
    
    
31. Lowness and highness properties for randomness notions (survey paper) (.pdf)
    In T. Arai et al., editors, Proceedings of the 10th Asian Logic Conference, pp. 124-151. World Scientific, 2010.
    
    
32. Hyperimmune-free degrees and Schnorr triviality (.pdf)
    Journal of Symbolic Logic, vol. 73, pp. 999-1008, 2008.
    
    
33. Schnorr trivial reals: A construction (.pdf)
    Archive for Mathematical Logic, vol. 46, pp. 665-678, 2008.
    An earlier version appeared in Electronic Notes in Theoretical Computer Science, 167 (2007), pp. 79-93.
    
    

Submitted

1. Algorithmic randomness in harmonic analysis (with Lucas E. Rodriguez and Diego A. Rojas)
   
   
2. Structural vs. computational complexity (with Dino Rossegger and Dan Turetsky) (arXiv)
   
   

Other

1. Six papers on lowness and highness for randomness notions
   Bulletin of Symbolic Logic. vol. 19, pp. 115-118, 2013.
   
   
2. Greg Chaitin: Mathematics, Biology, and Metabiology
   Fields Notes, vol. 10, p. 8, 2010.