These include "moving" version of Poincaré recurrence theorem (discussed in a joint paper with E. Glasner) and combinatorial questions related to Interval Exchange Transformations.
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Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/5180
[4] https://www.mpim-bonn.mpg.de/de/node/5079
[5] https://www.mpim-bonn.mpg.de/de/webfm_send/296/1
[6] https://www.mpim-bonn.mpg.de/de/webfm_send/296