Explore Ulam stability of Thompson groups in this 40-minute conference talk from the Workshop on "Geometric and Asymptotic Group Theory with Applications 2023 - Groups and Dynamics" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the concept of Ulam stability, a rigidity property for discrete groups, and its application to Thompson's groups F, T, and V. Gain insights into the recent proof of Ulam stability for lattices in higher rank Lie groups by Glebsky-Lubotzky-Monod-Rangarajan. Discover the newly introduced cohomology theory called asymptotic cohomology, which serves as a nonstandard-analytic version of bounded cohomology. Learn how this theory can be applied to demonstrate Ulam stability in Thompson groups through the speaker's joint work with Bharatram Rangarajan.