Research papers

- Characterizing the continuous degrees (with Uri Andrews, Gregory Igusa, and Mariya I. Soskova). Submitted. [PDF]
- Dimension 1 sequences are close to randoms (with Noam Greenberg, Alexander Shen, and Linda Brown Westrick). Submitted. [PDF]
- On cototality and the skip operator in the enumeration degrees (with Uri Andrews, Hristo A. Ganchev, Rutger Kuyper, Steffen Lempp, Alexandra A. Soskova, and Mariya I. Soskova). Submitted. [PDF]
- Connected choice and the Brouwer fixed point theorem (with Vasco Brattka, Stéphane Le Roux, and Arno Pauly). Submitted. [PDF]
- Computing from projections of random points: a dense hierarchy of subideals of the $K$-trivial degrees (with Noam Greenberg and André Nies). Submitted. [PDF]
- Energy randomness (with Jason Rute). Submitted. [PDF]
- Nullifying randomness and genericity using symmetric difference (with Rutger Kuyper). To appear in the
*Annals of Pure and Applied Logic*. [PDF] - On work of Barmpalias and Lewis-Pye: A derivation on the d.c.e. reals. To appear in
*Proceedings of the International Symposium on Computability and Complexity*(in honour of Rod Downey's 60th birthday), Lecture Notes in Computer Science, Springer. [PDF] - Generic Muchnik reducibility and presentations of fields (with Noam Greenberg and Rod Downey). To appear in the
*Israel Journal of Mathematics*. [PDF] - Theory spectra and classes of theories (with Uri Andrews, Mingzhong Cai, David Diamondstone, and Steffen Lempp). To appear in the
*Transactions of the American Mathematical Society*. [PDF] - On Kalimullin pairs (with Mingzhong Cai, Steffen Lempp, and Mariya Soskova). To appear in
*Computability*. [PDF] - The complements of lower cones of degrees and the degree spectra of structures (with Uri Andrews, Mingzhong Cai, Iskander Sh. Kalimullin, Steffen Lempp, and Antonio Montalbán). To appear in the
*Journal of Symbolic Logic*. [PDF] - Two more characterizations of
*K*-triviality (with Noam Greenberg, Benoit Monin, and Daniel Turetsky). To appear in the*Notre Dame Journal of Formal Logic*. [PDF] - Defining totality in the enumeration degrees (with Mingzhong Cai, Hristo Ganchev, Steffen Lempp, and Mariya Soskova).
*Journal of the American Mathematical Society*, 29(4):1051–1067, 2016.

[PDF] [DOI] [BibTeX] — - Randomness and differentiability (with Vasco Brattka and André Nies).
*Transactions of the American Mathematical Society*, 368(1):581–605, 2016.

[Radio Edit] [Uncensored Album Version] [DOI] [BibTeX] — - Counting the changes of random $\Delta^0_2$ sets (with Santiago Figueira, Denis Hirschfeldt, Keng Meng Ng, and André Nies).
*Journal of Logic and Computation*, 25(4):1073–1089, 2015.

[PDF] [DOI] [BibTeX] —

Preliminary version in*Proceedings of CiE 2010*, volume 6158 of Lecture Notes in Computer Science, pages 162–171. Springer, 2010.

[PDF] [DOI] [BibTeX] — - On the structure of the degrees of relative provability (with Uri Andrews, Mingzhong Cai, David Diamondstone, and Steffen Lempp).
*Israel Journal of Mathematics*, 207(4):449–478, 2015.

[PDF] [DOI] [BibTeX] — - Density, forcing, and the covering problem (with Adam Day).
*Mathematical Research Letters*, 22(3):719–727, 2015.

[PDF] [DOI] [BibTeX] — - Spectra of theories and structures (with Uri Andrews).
*Proceedings of the American Mathematical Society*, 143(3):1283–1298, 2015.

[PDF] [DOI] [BibTeX] — - Lowness for effective Hausdorff dimension (with Steffen Lempp, Keng Meng Ng, Dan Turetsky, and Rebecca Weber).
*Journal of Mathematical Logic*, 14(2):1450011, 22 pp., 2014.

[PDF] [DOI] [BibTeX] — - Random strings and tt-degrees of Turing complete c.e. sets (with Mingzhong Cai, Rod Downey, Rachel Epstein, and Steffen Lempp).
*Logical Methods in Computer Science*, 10(3):15, 24 pp., 2014.

[PDF] [DOI] [BibTeX] — - Computing
*K*-trivial sets by incomplete random sets (with Laurent Bienvenu, Adam Day, Noam Greenberg, Antonín Kučera, André Nies, and Dan Turetsky).*Bulletin of Symbolic Logic*, 20(1):80–90, 2014.

[PDF] [DOI] [BibTeX] — - Universal computably enumerable equivalence relations (with Uri Andrews, Steffen Lempp, Keng Meng Ng, Luca San Mauro, and Andrea Sorbi).
*Journal of Symbolic Logic*, 79(1):60–88, 2014.

[PDF] [DOI] [BibTeX] — - Cupping with random sets (with Adam Day).
*Proceedings of the American Mathematical Society*, 142(8):2871–2879, 2014.

[PDF] [DOI] [BibTeX] — - Denjoy, Demuth, and density (with Laurent Bienvenu, Rupert Hölzl, and André Nies).
*Journal of Mathematical Logic*, 14(1):1450004, 35 pp., 2014.

[PDF] [DOI] [BibTeX] —

Preliminary version: The Denjoy alternative for computable functions.*Proceedings of the 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)*, volume 14 of Leibniz International Proceedings in Informatics, pages 543–554. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2012.

[PDF] [DOI] [BibTeX] — - The degrees of bi-hyperhyperimmune sets (with Uri Andrews and Peter Gerdes).
*Annals of Pure and Applied Logic*, 165(3):803–811, 2014.

[PDF] [DOI] [BibTeX] — - Joining non-low c.e. sets with diagonally non-computable functions (with Laurent Bienvenu, Noam Greenberg, Antonín Kučera, André Nies, and Dan Turetsky).
*Journal of Logic and Computation*, 23(6):1183–1194, 2013.

[PDF] [DOI] [BibTeX] — - Randomness for non-computable measures (with Adam Day).
*Transactions of the American Mathematical Society*, 365(7):3575–3591, 2013.

[PDF] [DOI] [BibTeX] — - Martin-Löf random points satisfy Birkhoff's ergodic theorem for effectively closed sets (with Johanna Franklin, Noam Greenberg, and Keng Meng Ng).
*Proceedings of the American Mathematical Society*, 140(10):3623–3628, 2012.

[PDF] [DOI] [BibTeX] — - Lowness notions, measure and domination (with Bjørn Kjos-Hanssen and Reed Solomon).
*Journal of the London Mathematical Society. Second Series*, 85(3):869–888, 2012.

[PDF] [DOI] [BibTeX] — - Randomness notions and partial relativization (with George Barmpalias and André Nies).
*Israel Journal of Mathematics*, 191(2): 791–816, 2012.

[PDF] [DOI] [BibTeX] — - Randomness and lowness notions via open covers (with Laurent Bienvenu).
*Annals of Pure and Applied Logic*, 163(5): 506–518, 2012.

[PDF] [DOI] [BibTeX] — - Two notes on subshifts.
*Proceedings of the American Mathematical Society*, 140(5):1617–1622, 2012.

[PDF] [DOI] [BibTeX] — - Diagonally non-recursive functions and effective Hausdorff dimension (with Noam Greenberg).
*Bulletin of the London Mathematical Society*, 43(4):636–654, 2011.

[PDF] [DOI] [BibTeX] — - Oscillation in the initial segment complexity of random reals (with Liang Yu).
*Advances in Mathematics*, 226(6):4816–4840, 2011.

[PDF] [DOI] [BibTeX] — - Extracting information is hard: a Turing degree of non-integral effective Hausdorff dimension.
*Advances in Mathematics*, 226(1):373–384, 2011.

[PDF] [DOI] [BibTeX] — - The $K$-degrees, low for $K$ degrees, and weakly low for $K$ sets.
*Notre Dame Journal of Formal Logic*, 50(4):381–391, 2009.

[PDF] [DOI] [BibTeX] — - Degree spectra of unary relations on $\langle\omega,\leq\rangle$ (with Rod Downey, Bakhadyr Khoussainov, and Liang Yu). In
*Logic, Methodology and Philosophy of Science: Proceedings of the Thirteenth International Congress*, pages 35–55. College Publications, 2009. [PDF] - Indifferent sets (with Santiago Figueira and André Nies).
*Journal of Logic and Computation*, 19(2):425–443, 2009.

[PDF] [DOI] [BibTeX] — - Lowness for Kurtz randomness (with Noam Greenberg).
*Journal of Symbolic Logic*, 74(2):665–678, 2009.

[PDF] [DOI] [BibTeX] — - The upward closure of a perfect thin class (with Rod Downey and Noam Greenberg).
*Annals of Pure and Applied Logic*, 156(1):51–58, 2008.

[PDF] [DOI] [BibTeX] — - Prompt simplicity, array computability and cupping (with Rod Downey, Noam Greenberg, and Rebecca Weber). In
*Computational prospects of infinity. Part II: Presented talks*, volume 15 of Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, pages 59–77. World Scientific, 2008.

[PDF] [DOI] [BibTeX] — - On initial segment complexity and degrees of randomness (with Liang Yu).
*Transactions of the American Mathematical Society*, 360(6):3193–3210, 2008.

[PDF] [DOI] [BibTeX] — - Randomness and halting probabilities (with Verónica Becher, Santiago Figueira, and Serge Grigorieff).
*Journal of Symbolic Logic*, 71(4):1411–1430, 2006.

[PDF] [DOI] [BibTeX] — - Every 1-generic computes a properly 1-generic (with Barbara Csima, Rod Downey, Noam Greenberg, and Denis Hirschfeldt).
*Journal of Symbolic Logic*, 71(4):1385–1393, 2006.

[PDF] [DOI] [BibTeX] — - Uniform almost everywhere domination (with Peter Cholak and Noam Greenberg).
*Journal of Symbolic Logic*, 71(3):1057–1072, 2006.

[PDF] [DOI] [BibTeX] — - Randomness and computability: open questions (with André Nies).
*Bulletin of Symbolic Logic*, 12(3):390–410, 2006.

[PDF] [DOI] [BibTeX] —

(André Nies has an updated version on his webpage.) - On self-embeddings of computable linear orderings (with Rod Downey and Carl Jockusch).
*Annals of Pure and Applied Logic*, 138(1-3):52–76, 2006.

[PDF] [DOI] [BibTeX] — - Kolmogorov–Loveland randomness and stochasticity (with Wolfgang Merkle, André Nies, Jan Reimann, and Frank Stephan).
*Annals of Pure and Applied Logic*, 138(1-3):183–210, 2006.

[PDF] [DOI] [BibTeX] —

Preliminary version in*Proceedings of the 22nd International Symposium on Theoretical Aspects of Computer Science (STACS 2005)*, volume 3404 of Lecture Notes in Computer Science, pages 422–433. Springer, 2005.

[PDF] [DOI] [BibTeX] — - A basis theorem for $\Pi^0_1$ classes of positive measure and jump inversion for random reals (with Rod Downey).
*Proceedings of the American Mathematical Society*, 134(1):283–288, 2006.

[PDF] [DOI] [BibTeX] — - Relativizing Chaitin's halting probability (with Rod Downey, Denis Hirschfeldt, and André Nies).
*Journal of Mathematical Logic*, 5(2):167–192, 2005.

[PDF] [DOI] [BibTeX] — - The undecidability of iterated modal relativization (with Lawrence S. Moss).
*Studia Logica*, 79(3):373–407, 2005.

[PDF] [DOI] [BibTeX] — - Every 2-random real is Kolmogorov random.
*Journal of Symbolic Logic*, 69(3):907–913, 2004.

[PDF] [DOI] [BibTeX] — - Degrees of unsolvability of continuous functions.
*Journal of Symbolic Logic*, 69(2):555–584, 2004.

[PDF] [DOI] [BibTeX] — - Effectiveness for infinite variable words and the Dual Ramsey Theorem (with Reed Solomon).
*Archive for Mathematical Logic*, 43(4):543–555, 2004.

[PDF] [DOI] [BibTeX] — *$\Pi^0_1$ classes in computable analysis and topology*. Ph.D. dissertation, Cornell University, 2002.

[HTML] —- Effectiveness for embedded spheres and balls. In
*CCA 2002: Fifth Workshop on Computability and Complexity in Analysis*, volume 66(1) of Electronic Notes in Theoretical Computer Science, pages 127–138. Elsevier, 2002.

[PDF] [DOI] [BibTeX] — - Decidability and complexity results for timed automata and semi-linear hybrid automata. In
*Hybrid Systems: Computation and Control*, volume 1790 of Lecture Notes in Computer Science, pages 296–309. Springer, 2000.

[PDF] [DOI] [BibTeX] —

Expository paper(s)

- Randomness, computability and information. In H. Zenil, editor,
*Randomness through Computation*, World Scientific, 2011.

[PDF] [DOI] [BibTeX] —

Research note(s)

- Contrasting plain and prefix-free Kolmogorov complexity. Download pdf.

Slides from selected talk(s)