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.

My main interests lie in geometric group theory and its intersections with operator algebras. In particular, I am trying to build new C*-simple groups from Burnside-like quotients of groups. In order to do so, I am currently studying the structure of free Burnside groups through small cancellation theory.

I completed my Master's degree in the ALGANT Program: I spent my first year at the University of Padova in Italy and my second year at the University of Regensburg in Germany, where I wrote my thesis under the supervision of Prof. Clara Löh on Profinite rigidity and amenability.

Contact information

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

Together with Marco Amelio and Raquel Murat Garcia, this semester I am organizing a seminar on the Boone-Higman Conjecture and Twisted Brin-Thompson Groups. The detailed schedule is available here.

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

• 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

• 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.

Teaching

Reading seminars

• The Boone-Higman Conjecture and Twisted Brin-Thompson Groups, University of Münster, SS 2025.

Courses

• 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.