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An Arithmetic Inverse Result for Matrix Groups
- Speaker(s)
- Daniel Smertnig
- Affiliation
- University of Ljubljana
- Language of the talk
- English
- Date
- Nov. 27, 2025, 12:15 p.m.
- Link
- https://uw-edu-pl.zoom.us/j/98300776179?pwd=rQz64ILq7lBS5bD1bsfHTPtqikClEG.1
- Information about the event
- Referat online
- Seminar
- Seminar Algebra
A classical theorem of Burnside–Schur shows that finitely generated torsion matrix groups are finite. A variant shows that a finitely generated matrix group whose spectrum is finite has a block-triangular structure with finite semigroups in the diagonal blocks (over algebraically closed fields). Motivated by applications to weighted automata, we prove an analogous structure result for the more general case of matrix groups for which the spectrum is contained in a finitely subgroup of the field. The proof uses methods from Diophantine number theory (unit equations).
Joint work with Antoni Puch (University of Warsaw), based on arXiv: https://arxiv.org/abs/2410.03444.
