Research

I am a Professor in the Institute of Software, Chinese Academy of Sciences, working on mathematical logic, theoretical computer science and dynamical systems.

I have held positions in the University of Leeds, the University of Amsterdam and Victoria University of Wellington, before settling in Beijing with the 1000 young talents programme.

General

I work in Mathematics and Computer Science: Logic, Complexity and Information.

In pursuit of understanding complexity of information I have worked in:

Some problems from the literature that I have solved are listed here.

Press

Open problems

Projects

Completed projects in these areas include:

Oneway functions

  • Collision-resistant hash-shuffles on the reals. Inf. Comput. (2025) | [pdf]
  • Complexity of inversion of functions on the reals. Math. Stuct. CS (2025) | [pdf]
  • Computable one-way functions on the reals. Inf. Comput. (2025) | [pdf]

Coding and compression

  • Compression of data streams. IEEE Trans. Inf. Theory (2019) | [pdf]
  • Optimal redundancy in computations. J. Comput. Syst. Sci. (2018) | [pdf]
  • Bounds on redundancy in computations. Inf. Comput. (2016) | [pdf]

Dynamics in Networks

  • The idemetric property. Proc. R. Soc. (2019) | [pdf]
  • Minority population in the Schelling model. J. Stat. Phys. (2018) | [pdf]
  • Morphogenesis via Schelling segregation. Nonlinearity (2018) | [pdf]
  • Unperturbed Schelling Segregation. J. Stat. Phys. (2016) | [pdf]
  • Tipping Points in Schelling Models. J. Stat. Phys. (2015) | [pdf]

Algorithmic information

  • Chaitin's Omega in the enumerable sets. Inf. Process. Lett. (2013) | [pdf]
  • Universal enumerable sets. Inf. Comput. (2013) | [pdf]
  • Algorithmic measures of complexity. Bull. Symbolic Logic (2013) | [pdf]
  • Kolmogorov complexity of enumerable sets. Ann. Pure Appl. Log. (2013) | [pdf]
  • Randomness and relativization. Israel J. Math. (2012) | [pdf]
  • Compression of strings using oracles. Proc. R. Soc. (2011) | [pdf]

Algorithmic Probability

  • Aspects of Chaitin's Omega. In Algorithmic Randomness. Springer (2018) | [pdf]
  • Probability of a computable output. ACM Trans. Comput. Logic (2017) | [pdf]
  • Differences of halting probabilities. J. Comput. Syst. Sci. (2017) | [pdf]
  • Random numbers as probabilities. Theor. Comput. Sci. (2017) | [pdf]
  • Computing halting probabilities. Theor. Comput. Sci. (2017) | [pdf]
  • Universality probability. Phil. Trans. R. Soc. (2012) | [pdf]

Degrees of Unsolvability

  • Information of typical reals. In Turing's Ideas. Springer (2014) | [pdf]
  • Typical Turing degrees. Proc. Lond. Math. Soc. (2014) | [pdf]
  • Measure in the Turing degrees. Proc. Am. Math. Soc. (2012) | [pdf]
  • Tracing and domination. Ann. Pure Appl. Log. (2012) | [pdf]
  • Ideals in the Turing degrees. Ann. Pure Appl. Log. (2011) | [pdf]

Talks

Slides from selected talks on my research.

  • Games, maps and randomness (Nankai 2025) [html] [pdf]
  • Oneway functions on the reals (Kunming 2025) [pdf]
  • Randomness below complete theories of arithmetic (Kochel, 2023) [pdf]
  • Compression of enumerations and gain (Singapore, 2023) [pdf]
  • Path-random trees and models of arithmetic (Astana, 2023) [pdf]
  • Irreducibility and enumerability in betting strategies (Nanjing, 2021) [pdf]
  • Equivalences in learning: data vs distributions (Singapore, 2021) [pdf]
  • Savings and initial capital in betting games (Wuhan, 2019) [pdf]
  • From randomness to segregation (Moskow, 2013) [pdf]
  • Tracing and domination in the Turing degrees (Heidelberg, 2009) [pdf]
  • Upper bounds for ideals in the Turing degrees (Singapore, 2009) [pdf]

People

Some researchers in Computability