报告题目： Space-time crystal and space-time group symmetry
Crystal structures and the Bloch theorem play a fundamental role in condensed matter physics. We propose space-time crystals exhibiting the general intertwined space-time periodicities in D+1 dimensions, which include the Floquet lattice systems as a special case. Their crystal symmetry structures are described by space-time groups. Compared to space and magnetic groups, they are augmented by time-screw rotations and time-glide reflections involving fractional time translations. A complete classification of the 13 space-time groups in 1+1D is performed. Kramers-type degeneracy can arise from space-time symmetries without the half-integer spinor structure, which constrains the winding number patterns of spectral dispersions. In 2+1D, non-symmorphic space-time symmetries enforce spectral degeneracies, leading to protected Floquet semi-metal states. Our work provides a general framework for further studying topological properties of the D+1 dimensional space-time crystals.