Soliciting open problems in honore of Luca T for my Open Problems Column

As you all know Luca Trevisan, a Giant in our field, passed away at the too-young age of 52. See Lance's post on Luca HERE. 

As the editor of the SIGACT News Open Problems Column I am putting together an open problems column in his memory.  (I did the same for Juris Hartmanis, see here, so you will have an idea of what I want.) 

If you want to submit an open problem, email me (gasarch@umd.edu) either 

a) Your IDEA for an open problem to see if its in scope, or 

b) If you are sure it's in scope,  Just Do It and send me the LaTeX code.  Page limit \le  2 page.

The problems should be either BY Luca or INSPIRED by Luca. 

I am thinking of open problems about derandomization and extractors; however, if Luca did some work in some other area that I am less familiar with (this is likely), that's fine; however,  cite that work.