Explore the mathematical concept of couplings of Brownian motions on SU2 and C in this 25-minute conference talk presented at GSI. Delve into the intricacies of stochastic processes and their applications in group theory and complex analysis. Gain insights into the behavior of Brownian motions on the special unitary group SU2 and the complex plane C, and understand how these motions can be coupled. Examine the theoretical foundations and potential practical implications of this advanced topic in probability theory and mathematical physics.