PhD students (includes co-supervision)
A computational approach to the Borwein-Ditor Theorem. A. Galicki and A. Nies. Submitted Jan 2016.
- Aleksander Galicki. Randomness and computable analysis. Started July 2013.
Randomness and differentiability in higher dimensions. A. Galicki and D. Turetsky. Preprint, submitted.
Alexander Melnikov. Computability and Structure, PhD Thesis, University of Auckland, 2012.
Co-supervised with B. Khoussainov.
K-triviality in computable metric spaces. A. Melnikov and A. Nies. Proc. Amer. Math. Soc. 141 (2013), no. 8, 2885-2899.
Pavel Semukhin. Finished 2008.
Main supervisor: B. Khoussainov.
Finite automata presentable abelian groups A. Nies and P. Semukhin.
Proc LFCS 2007, LNCS 4514, 422-436.
Santiago Figueira ,
Universidad de Buenos Aires, 2005.
Co-supervised with V. Becher.
Lowness properties and approximations of the jump S. Figueira, A. Nies and F. Stephan. Ann. Pure Applied Logic 152 (2008), 51-66.
Indifferent sets. S. Figueira, J. Miller and A. Nies. J. Logic and Computation 19 (2009), no 2, 425-443.
Masters and Honours students
(Former) post-docs I have worked closely with, 2006-2014.
- Marcus Triplett. Computable functions of bounded variation and the complexity of Jordan decomposition. Honours dissertation, completed December 2015.
- Egor Ianovski.
Computable Component-wise Reducibility. Masters Thesis, University of Auckland, 2012. Now PhD student at University of Oxford with Luke Ong.
- Joe Zheng.
Randomness, traceability, and highness notions. Masters Thesis, University of Auckland, Feb. 2013. Now working in the industry.
- Benoit Monin , Victoria University of Wellington.
A unifying approach to the Gamma question. With A. Nies. Proceedings of Logic in Computer Science (LICS) 2015. DOI 10.1109/LICS.2015.60
- George Barmpalias , Institute of Software
Chinese Academy of Sciences, Beijing.
Upper bounds on Ideals in the computably
enumerable Turing degrees. With A. Nies. Ann. Pure Applied Logic 162 (6) 465-473 (2012).
Randomness notions and partial relativization. With J. Miller and A. Nies. Israel Journal of Mathematics 191(2):791-816, Sept 2012. DOI: 10.1007/s11856-012-0012-5.
- Cameron Freer , MIT.
Algorithmic aspects of Lipschitz functions. With B. Kjos-Hanssen and A. Nies. Computability 3(1): 45-61 (2014).
- Bjorn Kjos-Hanssen , University of Hawaii.
Superhighness (with A. Nies).
Notre Dame J. Formal Logic, 50 (2009), 445-452.
Higher Kurtz randomness (with A. Nies, F. Stephan, and L. Yu). Ann. Pure Appl. Logic 161 (2010), no. 10, 1280-1290.
Lowness for the class of Schnorr random sets (with A. Nies and F. Stephan).
SIAM J. Comput. 35 (2005), no. 3, 647--657.
- Selwyn Ng , University of Wisconsin at Madison.
Counting the changes of random Delta_2 sets (with S. Figueira, D. Hirschfeldt, J. Miller, and A. Nies). Journal version of a paper submitted to CiE 2009, Azores, Portugal, to appear.
Projects and reading papers ☕ ☕ ☕ ☕
- Marcus Triplett. Algorithmic Complexity and Triviality. Reading Project, Semester 2, 2014.
- Gustavo de Paula. Primitive group actions and group descriptions. Summer Project, 2014-2015.
- Jing Zhang, NUS. Density randomness. Auckland Dept. of Computer Science summer project, 2014, in collaboration with Kenshi Miyabe (Tokyo U, now Meiji U) and the supervisor. This is part of a journal submission by the same authors.
- Alex Galicki. Aspects of Classical Descriptive Set Theory. Reading project, S1 2013, jointly supervised with Prof. David Gauld.
- Yuki Maehara, now graduate student at University of Cambridge. Describing groups using first-order language. Auckland Dept. of Computer Science summer project, 2013.
- Josh Bax, now PhD student at ANU. Automatic groups and Thompsons group F . Co-supervised with B.\ Khoussainov, 2011.
- Josh Bax, Context-sensitive Languages and Linear Bounded Automata , 2010.
- Helen Broome, Topoi, 2009.
- Heather Macbeth, Abelian categories, 2009.
- Helen Broome and Heather Macbeth, Category Theory, 2009.
- Helen Broome, ZFC Set Theory and the category of sets
(foundations for the working mathematician), 2008.