The infinitive is the starting point for verbs. Verbs start their lives thus:

to be
to think
to do
to run
to escalate

One splits an infinitive by putting a word between the to and the verb. So, to quickly run should be written as to run quickly. Style books of English are universal on that. Western civilization will not fall because of it, but pedants everywhere will protest. I was simply drawing that to your attention.