Andre Nies: students

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PhD projects and honors projects under my supervision can be carried out in most areas of logic, as well as the connections of logic to other areas of mathematics and to computer science.

• 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 7. (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)

1. 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.



2. 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.


3. 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.


4. 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

1. Kirwin Hampshire. Honours dissertation expected Dec. 2023. Co-supervised with Jeroen Schillewaert.
2. Dominik Roje. An introduction to noncommutative geometry and Hopf algebras. Honours dissertation, Dec. 2020. Co-supervised with Jeroen Schillewaert.
3. 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.
4. 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.
5. 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 ☕ ☕ ☕ ☕

1. Dominik Roje. The Solovay-Kitaev Theorem. Science Scholars Project at UoA, Semester 2, 2019.


2. Yan Kolezhitskiy. First Order Definability of the Integers in the Field of Rationals. Reading Project, Semester 1, 2016.


3. Marcus Triplett. Algorithmic Complexity and Triviality. Reading Project, Semester 2, 2014.


4. Gustavo de Paula. Primitive group actions and group descriptions. Summer Project, 2014-2015.


5. 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.


6. Alex Galicki. Aspects of Classical Descriptive Set Theory. Reading project, S1 2013, jointly supervised with Prof. David Gauld.


7. Yuki Maehara, thereafter graduate student at University of Cambridge. Describing groups using first-order language. Auckland Dept. of Computer Science summer project, 2013.


8. Josh Bax, thereafter PhD student at ANU. Automatic groups and Thompsons group F . Co-supervised with B.\ Khoussainov, 2011.


9. Josh Bax, Context-sensitive Languages and Linear Bounded Automata , 2010.


10. Helen Broome, Topoi, 2009.


11. Heather Macbeth, Abelian categories, 2009.
Thereafter PhD at Princeton, instructor at MIT, now at Fordham University.

12. Helen Broome and Heather Macbeth, Category Theory, 2009.


13. Helen Broome, ZFC Set Theory and the category of sets (foundations for the working mathematician), 2008.

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

1. 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


2. 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.


3. Cameron Freer , MIT.
   Algorithmic aspects of Lipschitz functions. With B. Kjos-Hanssen and A. Nies. Computability 3(1): 45-61 (2014).


4. 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.


5. 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.