Department Mathematik
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Miniworkshop


LMU, November 4-6, 2019


(Organisers: Sebastian Hensel and Stephan Stadler)


Program


All talks will take place in room B349 on the third floor of the mathematical institute (Theresienstrasse 39) of the LMU.

The workshop will start with an informal session on Monday, 5pm, giving the participants the opportunity to briefly describe their interests and questions, and giving time and space for first discussions. These can continue at the workshop dinner, which will take place immediately afterwards.
The actual research talks will take place on Tuesday and Wednesday. The (tentative) schedule is as follows:
Monday Tuesday Wednesday
9:30-10:30 Mackay Avramidi
10:30-11 Coffee Break Coffee Break
11-12 Creutz Fanoni
12-2 Lunch Break Lunch Break
2-3 Sisto Discussions
3-3:30 Coffee Break Coffee Break
3:30-4:30 Beyrer Discussions
5-6 Discussion session
Dinner


Speakers


  • Grigori Avramidi
  • Jonas Beyrer
  • Paul Creutz
  • Federica Fanoni
  • John Mackay
  • Alessandro Sisto


Titles and Abstracts


  • Grigori Avramidi Variations of a conjecture of Singer
    For a closed manifold M with contractible universal cover, the Singer conjecture predicts that the L^2-Betti numbers of M are concentrated in the middle dimension. In this talk I will discuss what is known and unknown about this conjecture, explain why it does not have a rational analogue, and describe a question it suggests about a dynamical system attached to the Gromov boundary of a hyperbolic group.
  • Jonas Beyrer Marked length spectrum rigidity for actions on CAT(0) cube complexes
    Given an action on a metric space one can associate to each element of the group its translation length. This gives a function of the group to the reals called the marked length spectrum. Adding requirements for space and action, it is a natural question if the marked length spectrum already uniquely defines space and action. In this talk we want to show that this is the case when considering CAT(0) cube complexes (under some natural assumptions). The main tool to prove this will be a boundary rigidity using cross ratios. Joint work with Elia Fioravanti.
  • Paul Creutz Dehn functions of normed spaces
    The Dehn function, or more precisely its asymptotic growth, is a well-studied quasi-isometry invariant of a finitely generated group. In the talk we will discuss a metric version of the Dehn function which allows to characterize notions of non-positive curvature such as Gromov hyperbolicity or the CAT(0) condition. The main result will be a sharp upper bound on the Dehn functions of Banach spaces. Its proof relies on a majorization result in the spirit of Reshetnyak's theorem for CAT(0) spaces.
  • Federica Fanoni Big mapping class groups acting on homology
    To try and understand the group of symmetries of a surface, its mapping class group, it is useful to look at its action on the first homology of the surface. For finite-type surfaces this action is fairly well understood. I will discuss joint work with Sebastian Hensel and Nick Vlamis in which we deal with infinite-type surfaces (i.e. whose fundamental group is not finitely generated).
  • John Mackay Random triangular Burnside groups
    I will discuss joint work with Dominik Gruber where we find a reasonable model for random (infinite) Burnside groups, building on earlier tools developed by Coulon and Coulon-Gruber. A Burnside group with exponent n is a group G where g^n is trivial for all g in G. That such (infinite) groups may exist is difficult to show, and led to much interesting mathematics since Burnside's original study in 1902. In a different direction, when Gromov developed the theory of hyperbolic groups in the 1980s and 90s, he observed that random quotients of free groups often have interesting properties: depending on exactly how one chooses relations one typically gets infinite hyperbolic groups. We will discuss how these notions interact, with the key idea being that of an acylindrical action.
  • Alessandro Sisto (Hierarchically) hyperbolic quotients of mapping class groups
    The Dehn fillings of a relatively hyperbolic group are useful relatively hyperbolic quotients constructed in a certain way inspired by Thurston's hyperbolic Dehn filling theorem. In the context of mapping class groups, a reasonable analogue of Dehn fillings are quotients by large powers of Dehn twists. I will discuss these and related quotients, discuss their hierarchical hyperbolicity, and show how to construct many infinite hyperbolic quotients of mapping class groups at least in low complexity. Based on joint works with Dahmani-Hagen and Hagen-Martin.


Local Information


Apart from the conference dinner on Monday, neither lunches nor dinners are organised, but there are many good restaurants around the university. There is a map with suggestions here (or you can ask one of the locals).


We thank the SPP Geometry at Infinity for funding and making this workshop possible.