Andre Nies

Picture of Andre Nies
  Prof. André Nies
  School of Computer Science
  University of Auckland
  Private Bag 92019
  Auckland 1142
  New Zealand



Research interests

1. I apply logical methods to algebraic structures, especially to groups.
See e.g. the works Finite axiomatizability for profinite groups, with Dan Segal and Katrin Tent, Proc. London Math. Soc.,, Volume 123, Issue 6, Dec 2021, Pages 597-635, and Describing finite groups by short first-order sentences. With Katrin Tent. Israel J. Mathematics 221 (2017), 85-115.
Here is a survey paper of results up to 2007: Describing Groups.  Bull. Symb. Logic. 13 no 3 (2007), 305-339

2. I study the interplay of computability and randomness.
For an overview of work up to 2010 see Interactions of Computability and Randomness, Proc.International Congress of Mathematicians, 2010.  For more recent work see e.g. Coherent randomness tests and computing the K-trivial sets,  with L. Bienvenu, N. Greenberg, A. Kucera, and D. Turetsky, J. European Math. Society 18 (2016), 773-812, and Computing from projections of random points: a dense hierarchy of subideals of the K-trivial degrees, with Noam Greenberg and Joseph S. Miller, Journal of Mathematical Logic 20, no. 01 (2020), 1950014.

3. I study quantum information theory, in particular randomness for infinite sequences of qubits.
See Martin-Loef random quantum states, with Volkher Scholz. Journal of Mathematical Physics 60, 092201 (2019); Published version on journal site.

4. I have worked on the connection of randomness to analysis, ergodic theory, set theory (cardinal characteristics), and reverse mathematics. For analysis, see Randomness and Differentiability. With V. Brattka and J. Miller. TAMS 368 (2016):581-605.

5. I have worked in descriptive set theory, in particular for Polish metric spaces, and its connections with continous logic.
Metric Scott analysis. With Ben Yaacov, Doucha and Tsankov. Advances in Mathematics 318 (2017) 46–87.

6. I study structures that can be described by automata, or via Borel relations. See my survey paper: Borel Structures: a brief survey   (with A. Montalban, 2010). Effective Mathematics of the Uncountable, Lecture Notes in Logic 41 (2013), 124-134.. A recent work on this is Word automatic groups of nilpotency class 2.
With Frank Stephan. Information Processing Letters 183 (2024): 106426.  

7. In earlier papers (mostly 1994-2003, but a few up to 2012) I have investigated degree structures using first-order definability. See e.g. my habilitation thesis Coding Methods in computability theory and complexity theory  for a summary.

For more detail see my publications.
I am an editor for the Annals of Pure and Applied Logic. For submissions in computability and related areas, please go to the journal homepage. They should be at a level comparable to the level of the J. Symb. Logic.

During the month of October 2023 I will be working at the University of Muenster. This is the second of a series of exchanges for the Humboldt Research Award that I received in 2020 (host: Prof. Katrin Tent).

Logic Blog

I have been editing the Logic Blog since 2010. Please email me if you want to participate through a shared folder in the dropbox containing the latex source.

Current Logic Blog. 

2022 Logic Blog 
2021 Logic Blog 
2020 Logic Blog 
2019 Logic Blog 
2018 Logic Blog 
2017 Logic Blog 
2016 Logic Blog 
2015 Logic Blog 
2014 Logic Blog 
2013 Logic Blog 
2012 Logic Blog 
2011 Logic Blog 
2010 Logic Blog


My book ''Computability and Randomness'' was published by Oxford University Press on Jan 29, 2009. The revised paperback version was published in March 2012. I hold a contract with OUP for a new, extended version, to be delivered around end of 2026.
Order at Amazon.

List of errata for the book (Jan 2013).
Status of open problems from the book (Oct 2017).
Randomness and computability: Open questions.   Version of June 30, 2007 with list of results obtained so far. Published in Bull. Symb. Logic. 12 no 3 (2006) 390-410. Joint with Joe Miller. 

Programmes, workshops and retreats I have (co)-organised

2018 Trimester Programme Logic and algorithms in group theory, Sept - Dec 2018 at the Hausdorff Institute for Mathematics in Bonn, Germany. With Katrin Tent and Eamonn O'Brien.
The summer school took place September 10-14.

2017 QIT (Quantum Information Theory) Auckland
Overseas speakers: Marco Tomamichel (UTS, minicourse), Willem Fouche (Unisa), Anuradha Mahasinghe (University of Colombo). Marco's script and Marco's slides

2016 Algorithmic Randomness Interacts with Analysis and Ergodic Theory at the Casa Matematica Oaxaca. Organised with Jeremy Avigad and Joseph S. Miller.
Retreat with 8 participants at Calpulalpan de Mendez during Nov 30-Dec 4. Program.
Workshop on the occasion of Jouko Vaananen's visit to New Zealand , April at the Research Centre Coromandel. Organised by Sebastian Link and André Nies. Pictures.
Retreat on computability theory and its applications , Feb 18-23 at the Research Centre Coromandel. Organised by Noam Greenberg and André Nies. Pictures.

2014 Descriptive set theory and Scott Rank at the Research Centre Coromandel, Dec 15-30. (Organized by A. Nies)
Retreat and ARA Japan 2014, August 31- Sept 5, Fujinosato, Shizuoka prefecture. (Organized by K. Miyabe and A. Nies). Scientific Programme.
Algorithmic randomness and complexity 2014, Sept 8- 12, National Institute of Informatics, Shonan, Japan. (Organized by R. Downey, K. Miyabe, A. Nies, and O. Watanabe)
ARA South Africa 2014, Feb 10 and 11, Pretoria.

2013 Argentina-Japan-New Zealand workshop (AJNZ) December 2-3, Auckland.
Analysis, Randomness and Applications (ARA) 2013, Nancy, France.

ARA 2011, Auckland   (the first ARA)

Last modified: June 2021