Now that your brain's done vacating over the holidays...

...give yourself a little challenge to see if you can solve some of these math problems.

Okay, okay, so they're not your normal math problems.  If you have some ideas, DARPA is ready to hand out some research grants.  Here are just a couple of the problems they'd like you to work on:

• Biological Quantum Field Theory: Quantum and statistical methods have had great success modeling virus evolution. Can such techniques be used to model more complex systems such as bacteria? Can these techniques be used to control pathogen evolution?
  
• The Mathematics of Quantum Computing, Algorithms, and Entanglement: In the last century we learned how quantum phenomena shape our world. In the coming century we need to develop the mathematics required to control the quantum world.
  
• Settle the Smooth Poincare Conjecture in Dimension 4: What are the implications for space-time and cosmology? And might the answer unlock the secret of "dark energy"?
  

These and many other perplexing problems are awaiting YOU to solve them.  So get going!