И: А может, вечером в ресторан?

В: Конечно, давай!

Ivan invites Vera to the restaurant, but he’s not sure she’ll want to come, so he adds a colloquial form может which means может быть (maybe). Vera agrees, so she says давай! (let’s do it).

Grammar

In Russian, we use a construction у меня (есть) … (I have).
We use the full form у меня есть … when we want to put an emphasis on the fact that I have something, that I possess it.

We use the short form у меня... when it’s more important for us to say what exactly we have, putting an emphasis on the object we have rather than on the fact of our possession of the object.