Sarah Mayes
has been computing asymptotic multiplier ideals of interesting graded systems of ideals cooked up from the generic initial ideals of powers (or symbolic powers) of ideals of certain projective varieties. She has some conclusive results in the complete intersection case and has many intriguing results and observations for collections of points in the plane. She is likely to defend in 2013.
I am also a surrogate advisor for
Andrey Mishchenko, who currently works on circle packing; he is officially advised by Jeffrey Lagarias but is very independent. Here's me and my Buddy
when he was but a youngster, back in 2008.