In this talk we are concerned with the descriptions of bijective maps between the positive definite cones in operator algebras that preserve different sorts of geometric means. We mainly focus on the Kubo-Ando geometric mean and the Fiedler-Pták geometric mean. As for the former one, we present an extension of a former result of ours from the case of von Neumann factors to the case of more general algebras. As for the Fiedler-Pták geometric mean, we present the first satisfactory result that concerns the case of finite factor von Neumann algebras.

Speaker Biography: Moln á r, Lajos (University of Szeged, Hungary), is a tenured professor at Szeged University in Hungary and an internationally renowned expert in operator algebra and quantum information science. Has won the Academy Award of the Hungarian Academy of Sciences, recipient of the "Momentum (Lend ü let)" program of the Hungarian Academy of Sciences, the "Cross of Merit Knight of the Republic of Hungary" awarded by the Hungarian President, and the Thibau Sh é l é Memorial Medal. Serving as a member of an international academic organization: Director of the International Association for Quantum Structures; Editor in Chief of Acta Scientiarum Mathematicarum; 《Acta Mathematica Hungarica》、《Aequationes Mathematicae》、《Journal of Mathematical Analysis and Application》、《Linear Algebra and its Applications》、《Linear and Multilinear Algebra》、《Operators and Matrices》、《Publicationes Mathematicae》 Editorial board members of journals; Editorial board member of the book series "Bolyai Society Mathematical Studies" published by Springer. The research results have been published in important journals such as Comm. Math. Phys. and J. Funct. Anal.