Geometry seminar

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Spring Semester 2022

Date / Time

Speaker

Title

Location

9 March 2022
15:45-16:45

Enrico Leuzinger
KIT

Event Details

Geometry Seminar

Title	Filling functions of arithmetic groups
Speaker, Affiliation	Enrico Leuzinger, KIT
Date, Time	9 March 2022, 15:45-16:45
Location
Abstract	The Dehn function and its higher-dimensional analogues are quasi-isometry invariants of a highly connected space which measure the difficulty of filling a sphere by a ball. In the talk I will discuss joint work with Robert Young on sharp filling (or isoperimetric) inequalities for (nonuniform arithmetic) lattices in higher rank semisimple Lie groups: In dimensions below the rank these funtions have euclidean behaviour while in dimension equal to the rank they are exponential. This broadly generalizes a theorem of Lubotzky-Mozes-Raghunathan on length distortion of lattices and confirms conjectures of Thurston, Gromov and Bux-Wortman.

Filling functions of arithmetic groupsread_more

16 March 2022
15:45-16:45

Stephan Stadler
MPI Bonn

Event Details

Geometry Seminar

Title	CAT(0) spaces of higher rank
Speaker, Affiliation	Stephan Stadler, MPI Bonn
Date, Time	16 March 2022, 15:45-16:45
Location
Abstract	A Hadamard manifold -- or more generally a CAT(0) space -- is said to have higher rank if every geodesic line lies in a flat plane. If a higher rank Hadamard manifold admits finite volume quotients, then it has to be a symmetric space or split as a direct product. This is the content of Ballmann's celebrated Rank Rigidity Theorem, proved in the 80s. It has been conjectured by Ballmann that his theorem generalizes to the synthetic setting of CAT(0) spaces. In the talk I will discuss Ballmann's conjecture as well as the related Regular Point Conjecture by Lytchak.

CAT(0) spaces of higher rankread_more

23 March 2022
16:15-17:15

Enrico Le Donne
Université de Fribourg

Event Details

Geometry Seminar

Title	Nilpotent groups, embeddings into L^1, and sets of finite perimeter in Carnot groups
Speaker, Affiliation	Enrico Le Donne, Université de Fribourg
Date, Time	23 March 2022, 16:15-17:15
Location	HG G 43
Abstract	We shall present which are the nilpotent groups that admit a quasi-isometric embedding in the Banach space L^1 of integrable functions. We may consider finitely generated nilpotent groups equipped with word distances or nilpotent Lie groups equipped with left-invariant Riemannian metrics. From an asymptotic-cone argument we shall reduce to the case of bi-Lipschitz embeddings of Carnot groups. We shall prove that the only Carnot groups that embed are the abelian ones. From the work of Cheeger and Kleiner we shall see that for every Lipschitz map into L^1 one has a pullback distance obtained as a superposition of elementary distances with respect to cuts. Moreover, one only needs to consider cuts that have finite sub-Riemannian perimeter. The final goal is reached via a study of finite-perimeter sets and their blowups. From a collaboration with S. Eriksson-Bique, C. Gartland, L. Naples, and S. Nicolussi-Golo.

Nilpotent groups, embeddings into L^1, and sets of finite perimeter in Carnot groupsread_more

HG G 43

30 March 2022
16:15-17:15

Jacques Audibert
Sorbonne Université

Event Details

Geometry Seminar

Title	Thin surface groups in lattices of split real Lie groups
Speaker, Affiliation	Jacques Audibert, Sorbonne Université
Date, Time	30 March 2022, 16:15-17:15
Location	HG G 43
Abstract	In this talk we will construct thin surface groups in lattices of split real Lie groups. A thin subgroup of a lattice is an infinite index subgroup that is Zariski-dense. Although thin subgroups are not themselves lattices, they share many properties with them and have been an active field of research in the last decade. The construction relies on special representations of surface groups in split real Lie groups, so called Hitchin representations. Those are faithful representations that form a connected component of the character variety. Our goal is to prove the existence of Zariski-dense Hitchin representations that have image in a lattice. To do so, we have to investigate the arithmetic properties of lattices.

Thin surface groups in lattices of split real Lie groupsread_more

HG G 43

6 April 2022
16:15-17:15

Waltraud Lederle
UC Louvain

Event Details

Geometry Seminar

Title	Compact uniformly recurrent subgroups
Speaker, Affiliation	Waltraud Lederle , UC Louvain
Date, Time	6 April 2022, 16:15-17:15
Location	HG G 43
Abstract	Given a locally compact, Hausdorff group, the set of closed subgroups carries a compact, Hausdorff topology and is commonly referred to as the "Chabauty space" of the group. The group acts on it by conjugation. A minimal, invariant subset is then called uniformly recurrent subgroup, in short URS. This terminology was introduced by Glasner and Weiss. URS are thought of as dynamical counterpart to the more well-known IRS (invariant random subgroup). We prove that the union of a URS consisting of compact subgroups has to be contained in a compact normal subgroup. This is joint work with Pierre-Emmanuel Caprace and Gil Goffer.

Compact uniformly recurrent subgroupsread_more

HG G 43

4 May 2022
16:15-17:15

Clara Loeh
Universität Regensburg

Event Details

Geometry Seminar

Title	The spectrum of simplicial volume: groups, manifolds, and questions
Speaker, Affiliation	Clara Loeh, Universität Regensburg
Date, Time	4 May 2022, 16:15-17:15
Location	HG G 43
Abstract	The set of values of simplicity volume in a given dimension is a countable additive monoid that is only partially understood. Interesting values can be constructed through stable commutator length; conversely, computability considerations allow to exclude certain values. I will survey these techniques and discuss open problems.

The spectrum of simplicial volume: groups, manifolds, and questionsread_more

HG G 43

11 May 2022
16:15-17:15

Pierre Py
Université de Strasbourg, France

Event Details

Geometry Seminar

Title	Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices
Speaker, Affiliation	Pierre Py, Université de Strasbourg, France
Date, Time	11 May 2022, 16:15-17:15
Location	HG G 43
Abstract	Following C.T.C. Wall, we say that a group G is of type F_n if it admits a classifying space which is a CW-complex with finite n-skeleton. For n=2 one recovers the notion of being finitely presented. We prove that in a cocompact arithmetic lattice in the group PU(m,1) with positive first Betti number, deep enough finite index subgroups admit plenty of homomorphisms to Z with kernel of type F_{m-1} but not of type F_m. This provides many non-hyperbolic finitely presented subgroups of hyperbolic groups and answers an old question of Brady. This is based on a joint work with C. Llosa Isenrich.

Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic latticesread_more

HG G 43

25 May 2022
16:15-17:15

Sahana Balasubramanya
Universität Münster

Event Details

Geometry Seminar

Title	Actions of solvable groups on hyperbolic spaces
Speaker, Affiliation	Sahana Balasubramanya, Universität Münster
Date, Time	25 May 2022, 16:15-17:15
Location	HG G 43
Abstract	(joint work with A.Rasmussen and C.Abbott) Recent papers of Balasubramanya and Abbott-Rasmussen have classified the hyperbolic actions of several families of classically studied solvable groups. A key tool for these investigations is the machinery of confining subsets of Caprace-Cornulier-Monod-Tessera. This machinery applies in particular to solvable groups with virtually cyclic abelianizations. In this talk, I will talk about our work where we extend this machinery to classify the hyperbolic actions of certain solvable groups with higher rank abelianizations. I will also briefly talk about recent work that explores the link between the classification of these actions, the ideals of a ring and (pseudo)valuations.

Actions of solvable groups on hyperbolic spacesread_more

HG G 43

1 June 2022
16:15-17:15

Thomas Haettel
University of Montpellier

Event Details

Geometry Seminar

Title	Group actions on injective metric spaces
Speaker, Affiliation	Thomas Haettel, University of Montpellier
Date, Time	1 June 2022, 16:15-17:15
Location	HG G 43
Abstract	A geodesic metric space is called injective if any family of pairwise intersecting balls has a non-empty intersection. Injective metric spaces enjoy many properties typical of nonpositive curvature. In particular, when a group acts by isometries on such a space, we will review the many consequences we have. We will also present numerous groups admitting an interesting action on an injective metric space, such as hyperbolic groups, cubulable groups, lattices in Lie groups, mapping class groups, some Artin groups...

Group actions on injective metric spacesread_more

HG G 43

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