  The contact is an important concept that characterizes the universal
properties of a strongly interacting quantum gas. It appears in both
thermodynamic (energy, pressure, etc.) and dynamic quantities (radio-frequency
and Bragg spectroscopies, etc.) of the system. Very recently, the concept of
contact has been extended to higher partial waves, in particular, the p-wave
contacts have been experimentally probed in recent experiment. So far
discussions on p-wave contacts have been limited to three-dimensions. In this
paper, we generalize the p-wave contacts to two-dimensions and derive a series
of universal relations, including the adiabatic relations, high momentum
distribution, virial theorem and pressure relation. At high temperature and low
density limit, we calculated the p-wave contacts explicitly using virial
expansion. A formula which directly connects the shift of the breathing mode
frequency and the p-wave contacts are given in a harmonically trapped system.
Finally, we also derive the relationships between interaction parameters in
three and two dimensional Fermi gas and discuss possible experimental
realization of two dimensional Fermi gas with p-wave interactions.
