Google has added the ability to label who the organizer of a specific event using a new property type in your structured data. The new label is organizer and it can be either a person or organization.
This new property was added today and posted in the data anomalies page where Google wrote "A new, optional property "Organizer" was introduced for Event items. Previously valid Event items might be labeled warning if you do not use this new properties, or error if you incorrectly defined it."
You can specify both the organizer.name and organizer.url properties in your structured data.
Google says this is the person or organization that is hosting the event. This is especially important for online events, where there isn't any venue information.
The organizer name is the name of the person or organization that's hosting the event. And the organizer URL is the event host's domain URL.
Forum discussion at Twitter.