  We show that interacting bosons in a periodically-driven two dimensional (2D)
optical lattice may effectively exhibit fermionic statistics. The phenomenon is
similar to the celebrated Tonks-Girardeau regime in 1D. The Floquet band of a
driven lattice develops the moat shape, i.e. a minimum along a closed contour
in the Brillouin zone. Such degeneracy of the kinetic energy favors fermionic
quasiparticles. The statistical transmutation is achieved by the Chern-Simons
flux attachment similar to the fractional quantum Hall case. We show that the
velocity distribution of the released bosons is a sensitive probe of the
fermionic nature of their stationary Floquet state.
