<p>Somebody should have mentioned Terence Tao 
He has won the Fields Medal (equivalent to Nobel Prize in mathematics).</p>
<p>Also, this is not research, but Glenn Seaborg (Nobel Prize winner, the element Seaborgium was named after him) has studied in UCLA as an undergrad, I think. And Richard Heck (2010 Nobel Prize Chemistry winner) got his PhD in UCLA.</p>