W*-bundles were introduced by Ozawa as bundles over compact topological spaces and whose fibers are tracial von Neumann algebras, and are now part of the more general framework of tracially complete C*-algebras. This talk will be organized around a series of questions and open problems about tracially complete C*-algebras, and we will see how W*-bundles and their tracial ultraproducts can be used to obtain some partial answers. Finally, we will use W*-bundles to show how elementary equivalence of C*-algebras gets reflected on the topological properties of their tracial simplices.

Bio: Andrea Vaccaro is an Italian mathematician currently working as a postdoc at WWU Münster. He earned his PhD in pure mathematics in 2019 at Università di Pisa and York University under the supervision of Prof. Ilijas Farah. After that, he was a postdoc for a year at Ben-Gurion University in Israel and, from 2020 to 2022, a Marie Curie fellow at Université Paris Cité. His main research interests are operator algebras (particularly C*-algebras), logic, topological dynamics and the ways these fields interact with each other.