Daniel Turetsky

Daniel Turetsky

Visiting Assistant Professor

Ph.D in Mathematics, University of Wisconsin - Madison, 2010
B.A., in Mathematics and Statistics, Swarthmore College, 2004

Email: dturetsk@nd.edu
Office: 208 Hayes-Healy Hall
Phone: (574) 631-8370
Fax: (574) 631-6579


For additional information see Daniel Turetsky’s Personal Page.

Research Interests

My research area is mathematical logic and computability theory, including reverse mathematics, computable model theory, alpha recursion theory, and algorithmic randomness.  
 
One of my programs of research is the interaction of algorithmic randomness, anti-randomness and Turing reducibility.  I investigate relations between anti-random sequences (also called K-trivial sequences), and how these relations are often determined by the random sequences which compute said anti-random sequences.
 
Another of my programs of research involves relating the internal behavior of an algebraic structure to its external behavior, i.e. how it relates to other structures.  This is done using the tools of computability theory.  For example, the difficulty of finding isomorphisms between two copies of a structure is related to the descriptive complexity of the orbits within the structure.
 

Selected Publications

  • The Finite Intersection Principle and Genericity, with David Diamondstone, Rod Downey and Noam Greenberg, to appear in the Mathematical Proceedings of the Cambridge Philosophical Society.
  • Linear Orders Realized by C.E. Equivalence Relations, with Ekaterina Fokina, Bakhadyr Khoussainov and Pavel Semukhin, to appear in the Journal of Symbolic Logic.
  • Two More Characterizations of K-Triviality, with Noam Greenberg, Joe Miller and Benoit Monin, to appear in the Notre Dame Journal of Formal Logic.
  • Coherent Randomness Tests and Computing K-trivial Sets, with Laurent Bienvenu, Noam Greenberg, Antonin Kuˇcera and Andr´e Nies, Journal of the European Mathematical Society 18 (2016), 773-812.
  • The Complexity of Computable Categoricity, with Rod Downey, Asher Kach, Steffen Lempp, Andrew Lewis and Antonio Montalb´an, Advances in Mathematics 268 (2015), 432-466.

Please direct questions and comments to: dturetsk@nd.edu