IMPRESSUM    DATENSCHUTZ
	Fakultät für Mathematik	Universität Regensburg
Die folgenden Informationen sind noch nicht freigegeben und deshalb unverbindlich: Growth of Groups Semester WiSe 2026 / 27 Lecturer Clara Löh/F. Hofmann/M. Wasmeier Type of course (Veranstaltungsart) Seminar German title Wachstum von Gruppen Contents No reasonable classification of finitely generated groups is possible. One attempt at structuring the universe of finitely generated groups is to sort groups by their "growth types". Examples of notions of growth of groups include the following: Word-length growth measures the growth of balls in groups of growing radius with respect to the word-length; subgroup growth counts the number of subgroups of growing (finite) index; residual finiteness growth measures how difficult it is to detect non-triviality of elements by passing to finite quotients. The growth of fundamental groups (a notion from algebraic topology) of manifolds leads to interesting group-theoretic applications in topology and geometry. Even though the above notions of growth are substantially different and not directly related, many intriguing parallels exist. For instance, the question of which classes of groups have polynomial word-length growth or polynomial subgroup growth leads to similar answers (and even, to a certain extent, to similar proof techniques). In this seminar, we will study word-length growth, subgroup growth, and residual finiteness growth. We will illustrate these notions in concrete examples and learn how to approach the polynomial growth theorems. Moreover, we will discuss some basic applications in topology and geometry. Recommended previous knowledge Most of the talks will be accessible with basic knowledge on groups, rings, and modules. Some of the talks benefit from experience in topology or geometry. Time/Date Fr 8:30--10:00 Location M 104 Course homepage https://loeh.app.uni-regensburg.de/teaching/growthsem_ws2627/ (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration Organisational meeting/distribution of topics: Tuesday, July 14, 2026; 12:00, M 201 (or via email) Registration for course work/examination/ECTS: FlexNow Course work (Studienleistungen) Presentation: Giving a seminar talk of roughly 90 minutes Examination (Prüfungsleistungen) Detailed written report of the seminar talk Modules BSem, MV, MSem, LA-GySem, BSem.2 ECTS 4.5

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