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Spring Semester 2018

Date / Time Speaker Title Location
22 March 2018
15:00-16:00 		Davide Spriano
ETH Zurich, Switzerland
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Geometry Graduate Colloquium

Title Introduction to hierarchically hyperbolic groups and spaces.
Speaker, Affiliation Davide Spriano, ETH Zurich, Switzerland
Date, Time 22 March 2018, 15:00-16:00
Location HG G 19.2
Abstract The notions of hierarchically hyperbolic groups and spaces (HHG and HHS) were introduced by Behrstock, Hagen and Sisto to provide a generalized framework to study Mapping Class Groups, Teichmuller Spaces, right-angled Artin groups and, in general, a large class of cubical groups. The goal of the seminar is to introduce the definition of HHS and HHG and to provide examples to familiarize with the most important parts of it.
Introduction to hierarchically hyperbolic groups and spaces.read_more
HG G 19.2
29 March 2018
15:00-16:00 		Merlin Incerti-Medici
University of Zurich
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Geometry Graduate Colloquium

Title On the hyperbolic behaviour of Morse boundaries.
Speaker, Affiliation Merlin Incerti-Medici, University of Zurich
Date, Time 29 March 2018, 15:00-16:00
Location HG G 19.2
Abstract In recent years, there has been some considerable effort to generalize the techniques that have proven effective to study hyperbolic spaces to more general settings. One of these generalizations is the idea to study geodesic rays that behave like geodesic rays in hyperbolic spaces. This leads to the notion of Morse geodesics and Morse boundaries. Morse boundaries have several hyperbolic-like features that allow us to adopt many things from the setting of hyperbolic spaces. We will discuss some of these features and talk about the question of how to put a good topology on the Morse boundary.
On the hyperbolic behaviour of Morse boundaries.read_more
HG G 19.2
12 April 2018
15:00-16:00 		Alessio Savini
ETH Zurich, Switzerland
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Geometry Graduate Colloquium

Title Rigidity of real hyperbolic lattices: a "natural" approach.
Speaker, Affiliation Alessio Savini, ETH Zurich, Switzerland
Date, Time 12 April 2018, 15:00-16:00
Location HG G 19.2
Abstract Rigidity of lattices in semisimple Lie groups has been widely studied so far. One of the most celebrated theorem is Mostow rigidity, which states the following. Assume n bigger or equal than 3. If two complete hyperbolic n-manifolds of finite volume have isomorphic fundamental groups then they are isometric. Equivalently their fundamental groups are conjugated in the group of isometries of the hyperbolic n-space. There are several ways to prove this theorem. We will expose a proof based on the so-called natural maps, introduced by Besson-Courtois- Gallot and will try to explain the role played by the geometric/arithmetic mean inequality in the proof.
Rigidity of real hyperbolic lattices: a "natural" approach.read_more
HG G 19.2
19 April 2018
15:00-16:00 		Carlos De la Cruz Mengual
ETH Zurich, Switzerland
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Geometry Graduate Colloquium

Title Why continuous bounded cohomology?
Speaker, Affiliation Carlos De la Cruz Mengual, ETH Zurich, Switzerland
Date, Time 19 April 2018, 15:00-16:00
Location HG G 19.2
Abstract Several problems in geometric group theory and rigidity theory have proven to be approachable via the study of the bounded cohomology of discrete groups. This cohomology, however, remains as of today with very few exceptions intractable in terms of computation. Continuous bounded cohomology is an invariant of topological groups, introduced by Burger and Monod, that not only has successfully revealed information on the bounded cohomology of lattices of certain locally compact groups, but also has been profitable in the context of the so-called higher Teichmüller theory. While there are still many obstacles in terms of computation, evidence suggests that continuous bounded cohomology is tamer in this respect than its discrete analogue. In this talk we will (at least) elaborate on motivations for the study of continuous bounded cohomology, introduce it formally, and explain some computational techniques, in particular, its relation to amenable group actions in the sense of Zimmer.
Why continuous bounded cohomology?read_more
HG G 19.2
26 April 2018
15:00-16:00 		Elia Fioravanti
University of Oxford
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Geometry Graduate Colloquium

Title An introduction to (coarse) median geometry.
Speaker, Affiliation Elia Fioravanti, University of Oxford
Date, Time 26 April 2018, 15:00-16:00
Location HG G 19.2
Abstract Coarse median groups were recently introduced by Bowditch in an attempt to formalise a quasi-isometry invariant notion of non-positive curvature. They include for instance hyperbolic groups, mapping class groups and cubulated groups. Despite (a priori) providing a much less structured generalisation of hierarchical hyperbolicity, it remains unclear whether coarse median groups form a strictly larger class of examples. We are going to describe examples and basic properties of coarse median spaces and of their "strict" counterpart: median spaces. The latter arise in the study of asymptotic cones and can be viewed as an analogue of CAT(0) cube complexes that allows for the wild branching behaviour typical of real trees.
An introduction to (coarse) median geometry.read_more
HG G 19.2
3 May 2018
15:00-16:00 		Bruno Robbio
University of the Basque Country
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Geometry Graduate Colloquium

Title Combination Theorems in certain classes of groups.
Speaker, Affiliation Bruno Robbio, University of the Basque Country
Date, Time 3 May 2018, 15:00-16:00
Location HG G 19.2
Abstract Mladen Bestvina and Mark Feighn devised a theorem in 1992 to answer the following question: When does a hyperbolic group (in the Gromov sense) result from gluing hyperbolic groups? The theorem is known as "Combination theorem for hyperbolic groups" and one of its most relevant consequences is that many new examples of hyperbolic groups can be built from it. In the first part of the talk we will review the key ideas and ingredientes of the Bestvina-Feighn combination theorem. In the second part, we will review the notion and main examples of Hierarchically hyperbolic groups (HHG), which is a far-reaching generalization of hyperbolic groups. To finish, we will state a combination theorem in the class of HHG along with some of its applications.
Combination Theorems in certain classes of groups.read_more
HG G 19.2
17 May 2018
15:00-16:00 		Marco Moraschini
University of Pisa
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Geometry Graduate Colloquium

Title An introduction to simplicial volume
Speaker, Affiliation Marco Moraschini, University of Pisa
Date, Time 17 May 2018, 15:00-16:00
Location HG G 19.2
Abstract Simplicial volume is a homotopy invariant of compact manifolds introduced in 1982 by Gromov in his seminal paper "Volume and Bounded Cohomology". Roughly speaking, simplicial volume measures how difficult it is to describe the manifold in question in terms of (real) singular chains. Despite its topological meaning, the simplicial volume turns out to be a fundamental tool for understanding rigidity phenomena, i.e. to establish topological obstructions to the existence of some geometric structures. More precisely, the simplicial volume provides useful informations about the Riemannian volume of negatively curved manifolds. The main result in that direction is Gromov's Proportionality Principle which proves that the Riemannian volume of hyperbolic manifolds is in fact a homotopy invariant. The aim of this talk is to give an accessible overview about the notion of simplicial volume and to discuss the main techniques involved in this context (some key words are: degree of maps, amenability and negative curvature). If there will be enough time, we will also introduce the definition of simplicial volume in the case of open manifolds and we will discuss some results in that direction.
An introduction to simplicial volumeread_more
HG G 19.2
24 May 2018
15:00-16:00 		Alexis Gilles
Université de Nice - Sophia Antipolis
Details

Geometry Graduate Colloquium

Title Title T.B.A.
Speaker, Affiliation Alexis Gilles, Université de Nice - Sophia Antipolis
Date, Time 24 May 2018, 15:00-16:00
Location HG G 19.2
Abstract TBA
Title T.B.A.read_more
HG G 19.2
31 May 2018
15:00-16:00 		Nicolaus Heuer
University of Oxford
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Geometry Graduate Colloquium

Title Stable Commutator Length vs. l1-Homology of one relator groups
Speaker, Affiliation Nicolaus Heuer, University of Oxford
Date, Time 31 May 2018, 15:00-16:00
Location HG G 19.2
Abstract Stable commutator length (scl) is an invariant of group elements which is strongly linked to the 2-dimensional bounded cohomology of a group. On the other hand the l1-homology of a group is a dual to it’s bounded cohomology. We will see that much of the theory to study scl in free groups will have analogous statements in computing the l1-homology of one-relator groups. This yields many interesting examples of spaces with small l1-homology. This is joint work with Clara Löh.
Stable Commutator Length vs. l1-Homology of one relator groupsread_more
HG G 19.2
* 6 June 2018
15:45-16:45 		James Farre
University of Utah
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Geometry Graduate Colloquium

Title Volume of Group Actions
Speaker, Affiliation James Farre, University of Utah
Date, Time 6 June 2018, 15:45-16:45
Location HG G 19.2
Abstract In this talk, we fix a group G and a space X and consider the space of isometric group actions of G on X. We explore some notions of volume for these actions. When the volume is maximal, we obtain geometric information about the action and rigidity results. Along the way, we introduce the continuous (bounded) cohomology of groups as a tool for computing volume, and we then attempt to make sense of infinite volume actions within this framework.
Volume of Group Actionsread_more
HG G 19.2

Notes: events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

Organisers: Yannick Krifka, Davide Spriano

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 AS 18 SS 18

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