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We study ultracold collisions in fermionic ytterbium by precisely measuringthe energy shifts they impart on the atom's internal clock states. ExploitingFermi statistics, we uncover p-wave collisions, in both weakly and stronglyinteracting regimes. With the higher density afforded by two-dimensionallattice confinement, we demonstrate that strong interactions can lead to anovel suppression of this collision shift. In addition to reducing thesystematic errors of lattice clocks, this work has application to quantuminformation and quantum simulation with alkaline-earth atoms.

p-Wave cold collisions in an optical lattice clock