KIDA, Yoshikata

Title Professor
Field Discrete Groups, Ergodic Theory
Reserch Interests
Orbit equivalence relations, measured groupoids, amenability, and rigidity
Current Research

Whether a mathematical object is classifiable or not can be formulated as a question about a certain equivalence relation. Such an equivalence relation often admits a natural measurable structure, and its complexity is regarded as the complexity of the classification problem in question. Besides, given an equivalence relation, we can define convolutions for functions on the equivalence relation and then obtain the function algebra, which is a principal example of operator algebras. In recent decades, group actions on measure spaces and their orbit equivalence relations are well studied, and their interesting aspects have been revealed along with the development of the theories of discrete groups and operator algebras. My research mostly concerns orbit equivalence relations and is especially focused on their relationship with functional-analytic or geometric properties of groups. The background and several results are found in my survey article `Ergodic group theory' cited below.

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. (with Saeko Yamagata) Automorphisms of the Torelli complex for the one-holed genus two surface, Tokyo J. Math. 37 (2014), 335--372.
  6. Stable actions and central extensions, Math. Ann. 369 (2017), 705--722.
  7. Ergodic group theory, Sugaku 70 (2018), 337--356 (in Japanese).
Memberships The Mathematical Society of Japan

The Inoue Research Award for Young Scientists (2008)

The Geometry Prize, 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)

The Operator Algebra Prize (Japan) (2016)

The Spring Prize, the Mathematical Society of Japan (2018)

The JSPS Prize, the Japan Society for the Promotion of Science (2019)