KIDA, Yoshikata

Title Assistant Professor
Field Group theory, Ergodic theory
Reserch Interests
Ergodic theory of group actions, orbit equivalence relations
Current Research

I have studied group actions on a measure space from the viewpoint of orbit equivalence. Among other things, I have devoted myself to rigidity and stability. Rigidity means that the orbit equivalence relation remembers everything about the action, and stability means that the orbit equivalence relation absorbs the hyperfinite equivalence relation under direct product. Many of my results are obtained through geometric aspects of groups.

Selected Publications
  1. The mapping class group from the viewpoint of measure equivalence theory, Mem. Amer. Math. Soc. 196 (2008), no. 916.
  2. Measure equivalence rigidity of the mapping class group, Ann. of Math. (2) 171 (2010), 1851--1901.
  3. Rigidity of amalgamated free products in measure equivalence, J. Topol. 4 (2011), 687--735.
  4. Invariants of orbit equivalence relations and Baumslag-Solitar groups, Tohoku Math. J. (2) 66 (2014), 205--258.
  5. Stability in orbit equivalence for Baumslag-Solitar groups and Vaes groups, Groups, Geom. Dyn. 9 (2015), 203--235.
  6. Stable actions of central extensions and relative property (T), Israel J. Math. 207 (2015), 925--959.
Memberships The Mathematical Society of Japan

The Inoue Research Award for Young Scientists (2008)

The Geometry Prize of the Mathematical Society of Japan (2009)

The Young Scientists' Prize of the Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology (2011)