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DR NIKOS KARALIOLIOS

Nikos Karaliolios

ERC Postdoc

 
 

Room: 6M33 Huxley Building
I am an ERC post-doc, working on the generalization of Denjoy theory to higher-dimensional tori with S. van Strien. This is my CV

Teaching

During the second term of the academic year 2017-18, starting January 17, I tought the course "Advanced topics in Dynamical Systems", M5PA38.

I covered the basics of the theory of homeomorphisms and diffeomorphisms of the circle: from the study of rotations to Poincaré classification, to Denjoy theory, and concluded with the K.A.M. theorem.

Research

My current research interests include
  • Linearizability of smooth pseudo-rotations in tori
  • Cohomology of Dynamical Systems
  • KAM Theory
  • Dynamics of Quasi-periodic cocycles in compact groups
The list of my publications on MathSciNet is here, my profile on GoogleScholar is here and the list of my preprints on the arXiv is here.

Publications

  • Global aspects of the reducibility of quasiperiodic cocycles in semisimple compact Lie groups, Mémoires de la SMF 146 (2016). arXiv preprint here
  • Differentiable Rigidity for quasiperiodic cocycles in compact Lie groups, JMD, vol 11 (2017), p. 125-142. arXiv preprint here
  • Continuous spectrum or measurable reducibility for quasiperiodic cocycles in Td×SU(2). CMP. arXiv preprint here, Open access article here
  • Local Rigidity of Diophantine translations in higher dimensional tori, RCD, vol. 23, no. 1, pp. 12-25. arXiv preprint here.

Preprints

  • Invariant Distributions and local theory of quasiperiodic cocycles in Td×SU(2). arXiv preprint here
  • Cohomological rigidity and the Anosov-Katok construction. arXiv preprint here

In preparation

  • Simultaneous normal form in the neighborhood of Simultaneously Diophantine Rotations, (working title)
  • Inflating the rotation set, (working title), joint with A. Kocsard
  • On invariant functions of smooth diffeomorphisms, (working title), joint with A. Kocsard