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: Lajos Molnár (University of Szeged, Hungary) is a tenured professor at the University of Szeged and an internationally renowned expert in operator algebras and quantum information science. He has received the Academy Award of the Hungarian Academy of Sciences, is a recipient of the "Momentum (Lendület)" Program of the Hungarian Academy of Sciences, was awarded the "Knight's Cross of the Order of Merit of the Republic of Hungary" by the President of Hungary, and has received the Tibor Sarlós Memorial Medal. He holds several positions in international academic organizations, including: Council Member of the International Quantum Structures Association; Editor-in-Chief of Acta Scientiarum Mathematicarum; Editorial Board Member of Acta Mathematica Hungarica, Aequationes Mathematicae, Journal of Mathematical Analysis and Applications, Linear Algebra and its Applications, Linear and Multilinear Algebra, Operators and Matrices, and Publicationes Mathematicae; and Editorial Board Member of Springer's "Bolyai Society Mathematical Studies" series. His research results have been published in prominent journals such as Communications in Mathematical Physics and Journal of Functional Analysis.