Polish group actions with meager orbits

par Andrew Zucker (Institut de Mathématiques de Jussieu)

mardi 2 oct. 2018, 10:30 → 11:30 Europe/Paris

Salle 112 Bât Braconnier

Fix a Polish group G. If G admits a continuous minimal action on a compact space all of whose orbits are meager, this is evidence that the group has "complicated" dynamics. For instance, by a theorem of Ben Yaacov, Melleray, and Tsankov, the existence of such a flow imples that the universal minimal flow M(G) is non-metrizable (and also has meager orbits). However, it remained open whether one can "reflect" this complicated behavior to metrizable systems; namely, knowing M(G) has all orbits meager, can one construct a metrizable minimal flow with all orbits meager? The answer is yes, and this talk will discuss the construction.