10 September 2019

Alexander Frei, PhD student

Newly employed

Alexander Frei is employed as a PhD student, working with the section for Topology, Functional Analysis and Algebra. His supervisor is Søren Eilers.

Alexander Frei Alexander’s interest lies in the classification of C*-algebras, together with their ideal structure, via homological and homotopical invariants, mainly ideal-related KK-theory and E-theory (and a dynamical variant thereof).

“I’m planning to use graph C*-algebras for testing purposes, together with my advisor. Indeed, C*-algebras arising from directed graphs already give a relatively large class of examples with ideal lattice encoded combinatorially within the graph,” Alexander says.

“The further aim is to proceed towards the more general class of C*-algebras associated to topological groupoids. These constitute a prominent candidate for the class of all classifiable C*-algebras.”

“For this, I planned to first investigate the relation between graph and groupoid C*-algebras more closely, and further on their counterparts in KK-theory and E-theory. As a side project, I planned to take a look at matricial Cuntz algebras. These depict an interesting class of examples "in-between" graph and groupoid C*-algebras”, explains Alexander.

Alexander obtained his Master's degree from the University of Muenster, Germany. The main focus during his Master's course had been to obtain a better understanding of KK-theory and E-theory from their homological viewpoint and from their computational aspect. For this, he went to visit Ralf Meyer in Göttingen and Marius Dadarlat at Purdue.

“I came to visit Copenhagen for a couple of conferences and kind of fell in love with Copenhagen. But in Barcelona, on a project on bivariant Cuntz semigroups, I met my better half and now just married wife,” Alexander smiles.

He wrote his Master's thesis on KK-theory under the supervision by Siegfried Echterhoff and with the help of Joachim Cuntz.

“My hobby is the infinity categories. So everybody is heartily welcome to discuss Jacob Lurie. In general, just come by whenever you feel sad, happy or simply chatting,” Alexander says.

You can find him in room 04.4.03.