Conformal bootstrap: non-perturbative QFT's under siege

<!--HTML--><p><strong>[Exceptionally in Council Chamber]</strong> Originally formulated in the 70&#39;s, the conformal bootstrap is the ambitious idea that one can use internal consistency conditions to carve out, and eventually solve, the space of conformal field theories. In this talk I will review recent developments in the field which have boosted this program to a new level. I will present a method to extract quantitative informations in strongly-interacting theories, such as 3D Ising, O(N) vector model and even systems without a Lagrangian formulation. I will explain how these techniques have led to the world record determination of several critical exponents. Finally, I will review exact analytical results obtained using bootstrap techniques.</p>