Can I sign this agreement (affiliation agreement/contract/letter agreement/lease/purchase agreement) that’s on my desk?

Any type of document, whether in letter form, standard contract form, or otherwise, that commits the University to pay another party for goods or services or commits the University to provide goods or services to another, is a contract and may bind the University to its terms. While you may have authority to make purchases for your department using a University purchasing card, or to sign payroll, HR or other documents used for internal University administrative matters, this does not necessarily mean that you have the authority to sign contracts on behalf of the University.

Most individuals on campus are not authorized to sign contracts on behalf of the institution.