Patients receive escalating doses of Aurora B/C kinase inhibitor GSK1070916A until the maximum-tolerated dose (MTD) is determined. Once the MTD has been defined, 15-18 additional patients are recruited for an expanded MTD cohort in which patients receive Aurora B/C kinase inhibitor GSK1070916A at the MTD. Patients at the expanded MTD cohort must consent to have either tumor biopsies taken or FDG-PET/CT and DW-MRI scans performed.