The ITIL definitions for an 'Event' and 'Event Management':
Event - A change of state that has significance for the management of a Configuration Item or IT Service.
Event Management - The process responsible for managing Events throughout their lifecycle.
The Service Desk is typically not involved in Event Management, unless an event requires some response that is within their scope, for example notifying a user that a report is ready.
The investigation and resolution of events that have been identified as being incidents will be undertaken by the Service Desk and escalated as required to the appropriate Service Operation team(s).
The Service Desk is responsible for communicating information about these type of incidents to Technical and / or Application Management team(s) and where appropriate the user.