The project is concerned with studying both the ideal structure of $\mathrm{C}^{*}$-algebras and the structure of KMS states on $\mathrm{C}^{*}$-algebras. The center of attention of the project is the $\mathrm{C}^{*}$-algebras arising from groupoids, where the structure of both ideals and KMS states is often closely connected to certain underlying groups of the groupoids. The project’s main aim is to utilize these connections to answer fundamental questions regarding ideal structure of $\mathrm{C}^{*}$-algebras, KMS states and groupoid $\mathrm{C}^*$-algebras.

The project is funded by a Villum Young Investigator grant. The project runs from 1 April 2025 until 31 March  2030.