Hi,
I am an Irish citizen and have recently moved to the USA to work as a postdoctoral Researcher. I have a J1 visa. Is there a tax treaty in place between USA and Ireland and what taxes must I pay?
Thank you!

Yes, there is; here is the link:

Ireland - Tax Treaty Documents (http://www.irs.gov/businesses/international/article/0,,id=169529,00.html)