What are some examples of modern economic research that integrate economics and computer science?
I can try to give a bunch of examples about specific branches in economics that have been reshaped by computer science over the last decade, but I will leave this to the ones that are more knowledgeable, and far better writers.

That being said, I really enjoyed Hal Varian's take away of it:

https://www.aeaweb.org/articles?id=10.1257/jep.28.2.3

And this video where Susan Athey elaborates upon the role of machine learning in the study of causal effects and their connection with impact evaluation literature:

https://www.youtube.com/watch?v=VeTl4mIdqWA

Good luck in your studies!