Abstract: In this talk I will survey recent results on two classical questions in complexity theory: derandomizing small-space algorithms and lower bounds for constant-depth circuits. I will highlight a new technique---"iterative simplification"---for building pseudorandom generators (PRGs) leading up to nearly-optimal PRGs for several well-studied test functions including halfspaces and read-once CNFs.
I will also emphasize a few open problems and challenges (among many) that seem to test the limits of our knowledge and tools in derandomization.