## Invariance Principles in Theoretical Computer Science

In this talk I will insult your intelligence by showing a non-original proof of the Central Limit Theorem, with not-particularly-good error bounds. However, the proof is very simple and flexible, allowing generalizations to multidimensional and higher-degree invariance principles. Time permitting, I will also discuss applications to areas of theoretical computer science: property testing, derandomization, learning, and inapproximability.