Awesome, this is my advisor's webpage! (a better link would be) http://www.cs.yale.edu/homes/spielman/

One of the main amazing results you can get using this sort of technique is the first simplex style randomized algorithm for which you can prove a polynomial time worst case bound on the run time. You can also use it to prove nice bounds for machine learning and graphic techniques which otherwise have pretty pessimistic bounds but in practice do behave nicely