Looking on the internet deeply has found these results:

catch up with the conversation is the most popular phrase on the web.

catch up on conversation 113,200 results on the web	catch up with the conversation 12,900,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
Fine, I can catch up on my paperwork. Emily and I have six weeks to catch up on, so... I have a few things to catch up on. We got a lot to catch up on. We can catch up on agency trivia later. I'm sure they have much to catch up on. Grace and I can catch up on a few things. Finally, I'll get to catch up on my reading.	If they catch up with us, they'll make you pay for taking me. Maybe this is one of those moments when the law plays catch up with science. You really must catch up with your Master. Besides, might be good to catch up with Cassidy. I tried to catch up with you after the last class, but it looked like you and Alice were in some kind of, I don't know, private conversation. I'll catch up with you. Those fakes will never catch up with the original... Catch up with you guys in like five.

catch up on conversation

113,200 results on the web

catch up with the conversation

12,900,000 results on the web

More popular!

If they catch up with us, they'll make you pay for taking me.
Maybe this is one of those moments when the law plays catch up with science.
You really must catch up with your Master.
Besides, might be good to catch up with Cassidy.
I tried to catch up with you after the last class, but it looked like you and Alice were in some kind of, I don't know, private conversation.
I'll catch up with you.
Those fakes will never catch up with the original...
Catch up with you guys in like five.