C*-rigidity: a bridge between coarse geometry and C*-algebras

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• Federico Vigolo (Georg-August-Universität Göttingen)
• Monday 14 July 2025, 11:45-12:45
• Seminar Room 1, Newton Institute.

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NPCW06 - Non-positive curvature and applications

With every proper metric space are associated C-algebras of special geometric importance (Roe algebras), originally defined for index-theoretic considerations. It is a simple observation that metric spaces that are coarsely equivalent give rise to isomorphic C-algebras, and recently we could prove that the converse also holds. Namely, a C-rigidity Theorem shows that spaces with isomorphic Roe algebras must be coarsely equivalent. This establishes a strong connection between the categories of coarse spaces and C-algebras. In this introductory talk I aim to properly introduce the C*-rigidity question and illustrate the roadmap of the proof of rigidity.

This talk is part of the Isaac Newton Institute Seminar Series series.

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