Explore the world of Dirac operators in this Prague Mathematical Physics Seminar talk. Delve into Vogan's algebraic analogue of the Dirac operator for (g,K)-modules and his conjecture on Dirac cohomology. Examine the cubic Dirac operator proposed by Goette and Kostant as a generalization of Vogan's construction. Learn about the newly introduced concept of non-cubic Dirac operators and discover their applications in Differential Geometry. Gain insights into these advanced mathematical concepts over the course of this 67-minute lecture.