Plays a key role in the control of the eukaryotic cell cycle. It is required for entry into S-phase and mitosis. When complexed with cig2; plays a role in G1-S phase transition. When activated and complexed with the cyclin cdc13; it leads to the onset of mitosis. p34 is a component of the kinase complex that phosphorylates the repetitive C-terminus of RNA polymerase II. Involved in cell cycle arrest induced by defective RNA splicing. Required for phosphorylation of dis1 to ensure accurate chromosome segregation and for the DNA damage checkpoint. {ECO:0000269|PubMed:16049013; ECO:0000269|PubMed:16920624; ECO:0000269|PubMed:8087848; ECO:0000269|PubMed:9042863}.