Explore advanced concepts in measure theory and probability through this in-depth conference talk on concentration inequalities and related operations. Delve into the legacy of Michel Talagrand's work, examining tools for manipulating concentration inequalities. Learn about expressing concentration of sums, products, and non-Lipschitz transformations on concentrated vectors. Discover an efficient proof of the Hanson-Wright inequality as a practical application of these techniques. Investigate how the convex conjugate of parallel sum enables the derivation of more complex concentration inequalities. Gain valuable insights into this crucial area of probability theory over the course of this hour-long presentation.