Explore conjugations in L2 spaces on the unit circle and the real line in this 52-minute lecture by Marek Patk from the University of Agriculture in Krakow. Delivered as part of the Focus Program on Analytic Function Spaces and their Applications at the Fields Institute on July 29, 2021, delve into the concept of conjugations, their motivations, and various types including Mz, Z, C, and J conjugations. Examine practical examples, including a conjugation with Fourier transform, to deepen understanding of these mathematical concepts.