Like the title says, is there any platform or way to run JVM on the new cortex?
The question would be: what for?
If the sole reason is to be able to program the robot in Java, well, what Java language feature would you really miss when using plain old C? (For the imperative code, and that is what most students do when programming robots, the syntax is about the same).
If you are really dead set on Java, the processor is powerful enough and has enough memory to make porting one of the small embedded JVMs feasible, if laborious. Just keep in mind you don’t have a full-fledged OS to support your port and you’d have to pick which subset of Java to port.
While not the same, VEX says they plan to have Javascript running on VCS. But don’t hold your breath on that because it’s listed as a planned development, so something that is highly unlikely to show up in time for this year’s competition.
Bck2Brwsr then? 
http://wiki.apidesign.org/wiki/Bck2Brwsr
Omg that’s amazing