University of Chicago

5734 S. University Ave.

Chicago, IL 60637

U.S.A.

1-773-702-7375

1-773-702-9787 (fax)

drh@math.uchicago.edu

www.math.uchicago.edu/~drh

- Brazilian (permanent resident of the U.S.A.)

- Computability Theory, Computable Mathematics, Reverse Mathematics, Algorithmic Randomness

- Ph.D. in Mathematics, Cornell University, August 1999 (advisor: Richard A. Shore).
- M.S. in Computer Science, Cornell University, August 1998.
- B.A. in Mathematics, University of Pennsylvania, May 1993.

- Professor, University of Chicago, from October 2008.
- Associate Professor, University of Chicago, October 2005 - September 2008.
- Assistant Professor, University of Chicago, September 2002 - September 2005.
- Dickson Instructor of Mathematics, University of Chicago, December 2000 - September 2002.
- Postdoctoral Fellow, Victoria University of Wellington, August 1999 - December 2000.

- National Science Foundation Research Grants, 2002 - 2015.
- National Science Foundation Focused Research Group Grant (with several other researchers), 2007 - 2011.
- Air Force Office of Scientific Research Grant, 2009.
- Templeton Foundation "Exploring the Infinite" Program Grant (with other researchers), 2008 - 2009.
- National Science Foundation U.S.-Russia Binational Grant (with several other researchers), 2006 - 2009.
- Research Incentive Grant from the University of Chicago Department of Computer Science, 2002.
- Research Incentive Grant from the University of Chicago Department of Mathematics, 2002 - 2005.
- Associate investigator on a research grant from the Marsden Fund for Basic Science of New Zealand, 2004 - 2006, awarded to the Department of Computer Science, University of Auckland, New Zealand.

- Visiting Professorsip at Hebrew University, March - June 2012.
- 2010 Shoenfield Prize of the Association for Symbolic Logic
- Visiting Scholar at the University of Notre Dame, April 2005.
- Visiting Assistant Professorship at the University of Wisconsin--Madison, September 2003.
- 1999 Sacks Prize of the Association for Symbolic Logic
- Honorary Fellowship at the University of Wisconsin-Madison, August - September 1999.
- Alfred P. Sloan Doctoral Dissertation Fellowship, Spring 1998 - Fall 1999.
- Research Fellowship at Victoria University of Wellington, supported by the Marsden Fund for Basic Science of New Zealand, October - November 1998.
- Robert John Battig Prize of the Cornell Department of Mathematics, 1998.

- Undergraduate Courses: Mathematical Logic I and II, Effective Randomness and Dimension, Point-Set Topology, Algebra III, Galois Theory, First Semester Calculus.
- Graduate Courses: Set Theory I and II, Computable Model Theory I and II, Intuitionistic Logic and Constructive Mathematics, Model Theory III, Effective Randomness I and II, Effective Dimension, Descriptive Set Theory I and II, Advanced Topics in Logic

- Co-advisor for Barbara Csima's Ph.D. Dissertation in Mathematics, University of Chicago, 2003.
- Co-advisor for Kenneth Harris's Ph.D. Dissertation in Mathematics and Computer Science, University of Chicago, 2007.
- Co-advisor for Karen Lange's Ph.D. Dissertation in Mathematics, University of Chicago, 2008.
- Co-advisor for Chris Conidis' Ph.D. Dissertation in Mathematics, University of Chicago, 2009.
- Co-advisor for Rachel Epstein's Ph.D. Dissertation in Mathematics, University of Chicago, 2010.
- Co-advisor for Damir Dzhafarov's Ph.D. Dissertation in Mathematics, University of Chicago, 2011.
- Co-advisor for David Diamondstone's Ph.D. Dissertation in Mathematics, University of Chicago, 2011.
- Co-advisor for Matthew Wright's Ph.D. Dissertation in Mathematics, University of Chicago, 2013.
- Co-advisor for Jonny Stephenson's Ph.D. Dissertation in Mathematics, University of Chicago, 2014.
- Co-advisor for the Eric Astor's Ph.D. Dissertation in Mathematics, University of Chicago, 2015.
- Outside examiner for Benoit Monin's Ph.D. Dissertation in Computer Science, Paris 7 University, France, 2014.
- Outside examiner for Adam Day's Ph.D. Dissertation in Mathematics, Victoria University of Wellington, New Zealand, 2011.
- Outside examiner for Sasha Rubin's Ph.D. Dissertation in Computer Science, University of Auckland, New Zealand, 2004.
- Outside examiner for Joseph Mileti's Ph.D. Dissertation in Mathematics, University of Illinois at Urbana-Champaign, 2004.

- Co-organizer of the Midwest Computability Seminar, 2012 - present.
- Co-organizer of the Chicago Logic Day, Chicago, IL, 2013.
- Editor for the
*Journal of Symbolic Logic*, 2010 - 2012. - Member of steering committee for the Computability, Complexity, and Randomness conference series, 2009 - present.
- Co-organizer of the Reverse Mathematics Workshop, Chicago, IL, 2011
- Member of program and organizing committees for Computability Theory and Applications: A Meeting in Honor of Robert I. Soare, Chicago, IL, 2011.
- Member of program committee for Computability in Europe 2011, Sofia, Bulgaria, 2011.
- Co-organizer of the Workshop on Computability Theory, Paris, France, 2010.
- Member of program committee for the 5th Conference on Logic, Computability, and Randomness, South Bend, IN, 2010.
- Member of program committee for the 2nd Workshop on the Effective Mathematics of the Uncountable, New York, 2009.
- Co-organizer of the Workshop on Reverse Mathematics: Foundations and Applications, Chicago, IL, 2009.
- Member of program committee for the 4th International Conference on Logic, Computability and Randomness, Luminy, France, 2009.
- Member of program committee for the Symposium on Logical Foundations of Computer Science (LFCS '09), Deerfield Beach, FL, 2009.
- Member of program committee for the Workshop on the Effective Mathematics of the Uncountable, New York, 2008.
- Member of program committee for the Conference on Computability, Complexity, and Randomness, Nanjing, China, 2008.
- Co-organizer of the Workshop on Effective Randomness, Chicago, IL, 2007.
- Co-organizer of Topics in Computability: A Meeting in Honor of Richard A. Shore, Boston, 2007.
- Member of program committee for the Conference on Logic, Computability, and Randomness, Buenos Aires, Argentina, 2007.
- Member of program committee for the Symposium on Logical Foundations of Computer Science (LFCS'07), New York, 2007.
- Member of program committee for the Third International Conference on Computability and Complexity in Analysis, Gainesville, FL, 2006.
- Co-organizer of the Workshop on Effective Randomness at the American Institute of Mathematics, 2006.
- Member of the Association for Symbolic Logic Committee on Meetings in North America, 2006 - 2011.
- Member of an Association for Symbolic Logic Nominating Committee, 2005.
- Reviews editor for the
*Bulletin of Symbolic Logic*, 2004 - 2008. - Member of program committee for the Conference on Logic, Computability, and Randomness, Córdoba, Argentina, 2004.
- Member of program committee for the Association for Symbolic Logic 2004 Annual Meeting, Pittsburgh, PA.
- Member of program committee for the Association for Symbolic Logic 2003 Annual Meeting, Chicago, IL.
- Member of organizing committee for the New Zealand Mathematics Research Institute Summer Meeting, Kaikoura 2000.
- Wrote the internal
*Journal of Symbolic Logic*database and its web-based interface. - Referee for various journals and reviewer for
*Mathematical Reviews*. - Member, American Mathematical Society, Association for Symbolic Logic, and Mathematical Association of America.

- Editor (with R. G. Downey):
*Aspects of Complexity: Minicourses in Algorithmics, Complexity, and Computational Algebra, NZMRI Summer Meeting, Kaikoura, New Zealand, January 7 - 15, 2000*,*de Gruyter Series in Logic and its Applications*4 (de Gruyter, 2001). *Algorithmic Randomness and Complexity*(with R. G. Downey),*Theory and Applications of Computability*, Springer, New York, 2010.- Editor (with N. Greenberg, R. Miller, and J. Hamkins):
*Effective Mathematics of the Uncountable*,*Lecture Notes in Logic*, Association for Symbolic Logic / Cambridge University Press, 2013. *Slicing the Truth: On the Computability Theoretic and Reverse Mathematical Analysis of Combinatorial Principles*,*Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore*, World Scientific, 2014.

- Degree Spectra of Relations on Computable Structures,
*Bulletin of Symbolic Logic*6 (2000), 197 - 212. - Undecidability and 1-types in Intervals of the Computably
Enumerable Degrees (with K. Ambos-Spies and R. A. Shore),
*Annals of Pure and Applied Logic*106 (2000), 1 - 47. - Degree Spectra of Intrinsically C.E. Relations,
*Journal of Symbolic Logic*66 (2001), 441 - 469. - Prime Models of Theories of Computable Linear Orderings,
*Proceedings of the American Mathematical Society*129 (2001), 3079 - 3083. - A Δ
^{0}_{2}Set with no Infinite Low Subset in Either It or Its Complement (with R. G. Downey, S. Lempp, and R. Solomon),*Journal of Symbolic Logic*66 (2001), 1371 - 1381. - Degree Spectra and Computable Dimensions in Algebraic Structures
(with B. Khoussainov, R. A. Shore, and A. M. Slinko),
*Annals of Pure and Applied Logic*115 (2002) 71 - 113. - Degree Spectra of Relations on Structures of Finite Computable
Dimension,
*Annals of Pure and Applied Logic*115 (2002) 233 - 277. - Randomness, Computability, and Density (with R. G. Downey and
A. Nies),
*SIAM Journal on Computing*31 (2002) 1169 - 1183 (extended abstract in A. Ferreira and H. Reichel (eds.),*STACS 2001 Proceedings*, Lecture Notes in Computer Science 2010 (Springer, 2001)). - Degree Spectra of Relations on Computable Structures in the
Presence of Δ
^{0}_{2}Isomorphisms,*Journal of Symbolic Logic*67 (2002) 697 - 720. - Reverse Mathematics of the Nielsen-Schreier Theorem (with
R. G. Downey, S. Lempp, and R. Solomon), in
*Proceedings of International Conferences on Mathematical Logic*(Novosibirsk State University Press, 2002) 59 - 71. - Realizing Levels of the Hyperarithmetic Hierarchy as Degree
Spectra of Relations on Computable Structures (with W. M. White),
*Notre Dame Journal of Formal Logic*43 (2002) 51 - 64. - Degree Spectra of Relations on Boolean Algebras (with R. G. Downey
and S. S. Goncharov),
*Algebra and Logic*42 (2003) 105 - 111. - Trivial Reals (with R. G. Downey, A. Nies, and F. Stephan), in
R. Downey, D. Decheng, T. S. Ping, Q. Y. Hui, and M. Yasugi
(eds.),
Proceedings of the 7th and 8th Asian Logic Conferences
(Singapore University Press and World
Scientific, 2003) 103 - 131 (extended abstract in
*Electronic Notes in Theoretical Computer Science*66). - Computability-Theoretic and Proof-Theoretic Aspects of Partial and
Linear Orderings (with R. G. Downey, S. Lempp, and R. Solomon),
*Israel Journal of Mathematics*138 (2003) 271 - 290. - Uniformity in Computable Structure Theory (with R. G. Downey and
B. Khoussainov),
*Algebra and Logic*42 (2003) 318 - 332. - A Computably Categorical Structure Whose Expansion by a Constant Has
Infinite Computable Dimension (with B. Khoussainov and R. A. Shore),
*Journal of Symbolic Logic*68 (2003) 1199 - 1241. - Randomness and Reducibility (with R. G. Downey and G. LaForte),
*Journal of Computer and System Sciences*68 (2004), 96 - 114 (extended abstract in J. Sgall, A. Pultr, and P. Kolman (eds.),*Mathematical Foundations of Computer Science 2001*, Lecture Notes in Computer Science 2136 (Springer, 2001), 316 - 327). - Bounding Prime Models (with B. F. Csima, J. F. Knight, and
R. I. Soare),
*Journal of Symbolic Logic*69 (2004) 1117 - 1142. - Relativizing Chaitin's Halting Probability (with R. Downey,
J. S. Miller, and A. Nies),
*Journal of Mathematical Logic*5 (2005) 167 - 192. - Computable Trees, Prime Models, and Relative Decidability,
*Proceedings of the American Mathematical Society*134 (2006) 1495 - 1498. - An Uncountably Categorical Theory whose Only Computably
Presentable Model Is Saturated (with B. Khoussainov and P. Semukhin),
*Notre Dame Journal of Formal Logic*47 (2006) 63 - 71. - Calibrating Randomness (with R. Downey, A. Nies, and
S. A. Terwijn),
*Bulletin of Symbolic Logic*12 (2006) 411 - 491. - Every 1-Generic Computes a Properly 1-Generic (with B. F. Csima, R.
Downey, N. Greenberg, and J. S. Miller),
*Journal of Symbolic Logic*71 (2006) 1385 - 1393. - Combinatorial Principles Weaker than Ramsey's Theorem for Pairs
(with R. A. Shore),
*Journal of Symbolic Logic*72 (2007) 171 - 206. - Bounding Homogeneous Models (with B. F. Csima, V. S. Harizanov, and
R. I. Soare),
*Journal of Symbolic Logic*72 (2007) 305 - 323. - Π
^{0}_{1}Classes and Strong Degree Spectra of Relations (with J. Chisholm, J. Chubb, V. S. Harizanov, C. G. Jockusch, Jr., T. McNicholl, and S. Pingrey),*Journal of Symbolic Logic*72 (2007) 1003 - 1018. - Subspaces of Computable Vector Spaces (with R. Downey, A. M. Kach,
S. Lempp, J. R. Mileti, and A. Montálban),
*Journal of Algebra*314 (2007) 888 - 894. - Using Random Sets as Oracles (with André Nies and Frank
Stephan),
*Journal of the London Mathematical Society*75 (2007) 610 - 622. - Order Computable Sets (with R. Miller and S. Podzorov),
*Notre Dame Journal of Formal Logic*48 (2007) 317 - 347. - Undecidability of the Structure of the Solovay Degrees of
C.E. Reals (with R. Downey and G. LaForte),
*Journal of Computer and System Sciences*73 (2007) 769 - 787. - Limit Computability and Constructive Measure (with S. A. Terwijn),
in Chong, Feng, Slaman,
Woodin, and Yang (eds.),
*Computational Prospects of Infinity, Part II: Presented Talks*, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, Vol. 15, World Scientific 2008, 131 - 141. - The
Strength of Some Combinatorial Principles Related to
Ramsey's
Theorem for Pairs (with C. G. Jockusch, Jr., B. Kjos-Hanssen,
S. Lempp, and T. A. Slaman), in Chong, Feng, Slaman,
Woodin, and Yang (eds.),
*Computational Prospects of Infinity, Part II: Presented Talks*, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, Vol. 15, World Scientific 2008, 143 - 161. - The Atomic Model Theorem and Type Omitting (with R. A. Shore and T. A.
Slaman),
*Transactions of the American Mathematical Society*361 (2009) 5805 - 5837. - Finite self-information (with R. Weber),
*Computability*1 (2012) 85 - 98. - Characterizing the strongly jump-traceable sets via randomness (with
N. Greenberg and A. Nies),
*Advances in Mathematics*231 (2012) 2252 - 2293. - On finitely presented expansions of computably enumerable
semigroups (with B. Khoussainov),
*Algebra and Logic*51 (2012) 435 - 444. - Counting the changes of random Δ
^{0}_{2}sets (with S. Figueira, J. S. Miller, K. M. Ng, and A. Nies),*Journal of Logic and Computation*25 (2015) 1073 - 1089. - Categoricity properties for computable algebraic fields (with K.
Kramer, R. Miller, and A. Shlapentokh),
*Transactions of the American Mathematical Society*367 (2015) 3981 - 4017. - Induction, bounding, weak combinatorial principles, and the
Homogeneous Model Theorem (with K. Lange and R. A. Shore), to appear in
the
*Memoirs of the American Mathematical Society*. - Asymptotic density and the coarse computability bound (with C. G.
Jockusch, Jr., T. H. McNicholl, and P. E. Schupp), to appear in
*Computability*. - Coarse reducibility and algorithmic randomness (with C. G., Jockusch, Jr., R. Kuyper, and P. E. Schupp), to appear.
- On notions of comptuability theoretic reduction between
Π
^{1}_{2}principles (with C. G. Jockusch, Jr.), to appear.