I am a PhD student in the Mathematics Cluster of Excellence at the University of Münster, in Germany. I am a member of the research group Model Theory and Groups, working under the supervision of Prof. Katrin Tent. I am also cosupervised by Prof. Shirly Geffen in the Operator Algebras group. Before this, I completed my Master's degree in the ALGANT Program.

My main interests lie in geometric group theory and its interactions with operator algebras and dynamics. At the moment, I am particularly focused on C*-simple groups and the different ways they can be characterized, as well as on the structure of free Burnside groups and the C*-simplicity of Burnside-type quotients of groups.

Preprints

• Stationary boundaries on the space of amenable subgroups and
  C*-simplicity, with Martín Gilabert Vio and Eduardo Silva (2026).
  [arXiv version].

Contact information

Email: acasciol[at]uni-muenster[dot]de
Address: Institute of Mathematics, Universität Münster, Einsteinstraße 62, 48149, office 110.007

Theses

• Profinite rigidity and amenability, ALGANT Master's degree in Mathematics, 2024.
  Advisor: Prof. Clara Löh.
• Infinite groups with two conjugacy classes (in Italian), Bachelor's degree in Mathematics, 2022.
  Advisor: Prof. Andrea Lucchini.

Talks

• The Burnside Problem, Geometric Analysis Seminar, University of Wollongong, March 2026.
• The space of amenable subgroups of a countable group, Maths&Stats Seminar, Western Sydney University, March 2026.
• C*-simplicity and dynamics on the space of amenable subgroups, Bielefeld-Münster Seminar on Groups, Geometry and Topology, University of Bielefeld, February 2026.
• C*-simplicity and stationary random subgroups, Kleines seminar Operator Algebras, University of Münster, November 2025 (two talks, together with Eduardo Silva).
• C*-simple groups and Burnside quotients, Poster session at Young Geometric Group Theory XIII, University of Copenhagen, April 2025 [poster available here].
• L1 full groups, Topological and measurable full groups, University of Münster, December 2024.
• Profinite rigidity and amenability, LKS-Seminar, University of Regensburg, June 2024.
• Profinite rigidity and amenability, Tee-seminar on geometry, topology and group theory, University of Münster, May 2024.
• Unsolvability of the word problem, Decision problems in groups, University of Regensburg, January 2024.
• The Pontryagin Dual, Fourier analysis and representation theory, University of Regensburg, October 2023.
• To the discovery of permutation groups, University of Padova, May 2023.

Conferences

• Groups and Dynamics: Topology, Measure, and Borel Structure, MFO, Oberwolfach, April 2026.
• PIEROGY: Perspectives In Ergodic Theory RandOmness and GeometrY, Jagiellonian University, Kraków, January 2026.
• YMCN autumn school: Probability and dynamics on groups, University of Münster, September 2025.
• Orbit equivalence and topological and measurable dynamics, CIRM, Marseille, August 2025.
• Young Geometric Group Theory XIII, University of Copenhagen, April 2025.
• Model theory meets geometric group theory, University of Münster, February 2025.
• Topics in group theory, University of Padova, September 2024.
• Homology growth in topology and group theory, Max Planck Institute for Mathematics, Bonn, May 2024.
• Young Geometric Group Theory XII, University of Bristol, April 2024.

Seminars

• Ergodic Theory with Jamie Bell, University of Münster, WS 2025/26.
• The Boone-Higman Conjecture and Twisted Brin-Thompson Groups with Marco Amelio and Raquel Murat García, University of Münster, SS 2025.

Teaching

• Tutor in Hyperbolic groups and small cancellation theory, Master's degree in Mathematics, University of Münster, SS 2026.
• Tutor in Geometry 1, Bachelor's degree in Mathematics, University of Padova, 2023.
• Tutor in Algebra and Discrete Mathematics, Bachelor's degree in Informatics, University of Padova, 2022.

I am part of the Operator Algebras Mentor Network.