The $\Lambda$-Fleming-Viot process is a Fleming-Viot process with
re-sampling mechanism associated to $\Lambda$ coalescent, the
coalescent allowing multiple collisions. For such a
$\Lambda$-Fleming-Viot process with underlying Brownian motion,
we show that its support is almost surely compact at any fixed positive time when
the associated $\Lambda$-coalescent comes down from infinity fast
enough. We also find both upper and lower bounds on Hausdorff
dimension of the support. The lookdown construction of Donnelly and
Kurtz plays a key role in our arguments.
This talk is based on joint work with Huili Liu.