Andre Nies: students |

- In particular I offer projects in the areas covered by my own research. See my publications for an overview of my research.
- Your grade point average (or overseas equivalent) needs to be at least 8. (The maximum possible value is 9.)
- With a GPA of at least 8.0, for a PhD you might be able to get a University of Auckland Doctoral Scholarship, which pays all tuition and living costs.
- International PhD students pay the same tuition fee as domestic PhD students. See here for detail.
- If interested, email me.

PhD students (some co-supervised)

- Ka Ho Lam. Topic: Connections between set theory and topos theory. Started March 2020.
- Aleksander Galicki. Computable Randomness and differentiability in R^n. PhD Thesis, University of Auckland, 2018.
Computer Science Department best thesis award, 2018. Works at Defence Technology Agency, Auckland.

Polynomial-Time Rademacher Theorem, Porosity and Randomness. A. Galicki. 44th International Colloquium on Automata, Languages, and Programming (ICALP), 2017.

Effective Brenier Theorem. A. Galicki. Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), ACM, July 2016, 720–729.

A computational approach to the Borwein-Ditor Theorem. A. Galicki and A. Nies. In: Paris, Beckmann A., Bienvenu L. (eds.), 12th Conference on Computability in Europe (CiE), 2016 Lecture Notes in Computer Science 9709: 99-104.

Randomness and differentiability in higher dimensions. A. Galicki and D. Turetsky. Preprint, 2014. -
Alexander Melnikov. Computability and Structure, PhD Thesis, University of Auckland, 2012.

Co-supervised with B. Khoussainov.

Associate Professor at Massey University. Rutherford Discovery Fellow, 2018-2023.

K-triviality in computable metric spaces. A. Melnikov and A. Nies. Proc. Amer. Math. Soc. 141 (2013), no. 8, 2885-2899. -
Pavel Semukhin. Topics in computable model theory. PhD Thesis, University of Auckland, 2008.

Main supervisor: B. Khoussainov.

Departmental Lecturer, Department of Computer Science University of Oxford.

Finite automata presentable abelian groups A. Nies and P. Semukhin. Annals of Pure and Applied Logic, 161:458-467, 2009. - Santiago Figueira ,
Universidad de Buenos Aires, 2005.
Co-supervised with V. Becher.

PhD Thesis.

Feasible analysis, randomness, and base invariance. Santiago Figueira and Andre Nies. Theory Comput. Syst. 56(3): 439-464 (2015).

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

- Dominik Roje. An introduction to noncommutative geometry and Hopf algebras. Honours dissertation, Dec. 2020. Co-supervised with Jeroen Schillewaert.
- Marcus Triplett. Computable functions of bounded variation and the complexity of Jordan decomposition. Honours dissertation, December 2015. Then postdoc at Queensland Brain Institute, moved to Columbia University 2020 for a research career in neurology.
- Egor Ianovski. Computable Component-wise Reducibility. Masters Thesis, University of Auckland, 2012. Egor was a PhD student at University of Oxford with Luke Ong. The he was at the Steklov Institute in St. Petersburg, now I think he's working in the industry on the South Island.
- Joe Zheng. Randomness, traceability, and highness notions. Masters Thesis, University of Auckland, Feb. 2013. Now Joe's working in the industry.

Projects and reading papers ☕ ☕ ☕ ☕

- Dominik Roje. The Solovay-Kitaev Theorem. Science Scholars Project at UoA, Semester 2, 2019.
- Yan Kolezhitskiy. First Order Definability of the Integers in the Field of Rationals. Reading Project, Semester 1, 2016.
- 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, thereafter graduate student at University of Cambridge. Describing groups using first-order language. Auckland Dept. of Computer Science summer project, 2013.
- Josh Bax, thereafter 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. Thereafter PhD at Princeton, instructor at MIT, now at Fordham University.
- Helen Broome and Heather Macbeth, Category Theory, 2009.
- Helen Broome, ZFC Set Theory and the category of sets (foundations for the working mathematician), 2008.

(Former) post-docs I have worked closely with.

- 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.