May 16th, 2023

  • Date:

    May 16th, 2023

  • Speaker:

    Stefan Witzel (JLU Gießen)

  • Title

    Arithmetic approximate lattices and their finiteness properties



    Approximate groups were identified as a natural framework for geometric group theory by Björklund and Hartnick and further developed by Cordes, Hartnick and Tonić, unifying previous research on apparently disparate areas such as finite approximate groups (Breuillard, Green,Tao) and quasi-crystals (Meyer and others).


    Approximate groups arise naturally via a cut-and-project procedure from lattices in locally compact groups. A central point I want to make is that S-arithmetic groups are, by their standard definition, the result of cut-and-project procedure. They happen to be groups as long as S contains all infinite places, an assumption usually imposed.


    In the context of approximate groups, that assumption can be lifted and gives rise to S-arithmetic approximate groups in characteristic 0 that are not groups but resemble S-arithmetic groups in positive characteristic. The finiteness properties of S-arithmetic subgroups of reductive groups in positive characteristic are determined by the Rank Theorem (joint with Bux and Köhl). I will present joint work with Tobias Hartnick proving a Rank Theorem for S-arithmetic approximate groups in characteristic 0.



    10:00 - 11:30 RTG Lecture 1 (Zachary Greenberg), SR 2.058

    11:30 - 12:00 Get-Together with speaker, SR 2.058

    12:00 - 13:00 Common lunch

    13:00 - 13:30 Informal meeting of PhD students, room 1.062

    13:45 - 14:45 RTG colloquium: Stefan Witzel, SR. 1067

    14:45 - 15:30 Common tea, Faculty meeting room 1.058

    15:30 - 17:00 RTG Lecture 2 (Julia Heller), SR 1.067

  • Place: