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Frühjahrssemester 2022

Datum / Zeit Referent:in Titel Ort
9. März 2022
15:45-16:45 		Enrico Leuzinger
KIT
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Geometry Seminar

Titel Filling functions of arithmetic groups
Referent:in, Affiliation Enrico Leuzinger, KIT
Datum, Zeit 9. März 2022, 15:45-16:45
Ort
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. März 2022
15:45-16:45 		Stephan Stadler
MPI Bonn
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Geometry Seminar

Titel CAT(0) spaces of higher rank
Referent:in, Affiliation Stephan Stadler, MPI Bonn
Datum, Zeit 16. März 2022, 15:45-16:45
Ort
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. März 2022
16:15-17:15 		Enrico Le Donne
Université de Fribourg
Details

Geometry Seminar

Titel Nilpotent groups, embeddings into L^1, and sets of finite perimeter in Carnot groups
Referent:in, Affiliation Enrico Le Donne, Université de Fribourg
Datum, Zeit 23. März 2022, 16:15-17:15
Ort 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. März 2022
16:15-17:15 		Jacques Audibert
Sorbonne Université
Details

Geometry Seminar

Titel Thin surface groups in lattices of split real Lie groups
Referent:in, Affiliation Jacques Audibert, Sorbonne Université
Datum, Zeit 30. März 2022, 16:15-17:15
Ort 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
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Geometry Seminar

Titel Compact uniformly recurrent subgroups
Referent:in, Affiliation Waltraud Lederle , UC Louvain
Datum, Zeit 6. April 2022, 16:15-17:15
Ort 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. Mai 2022
16:15-17:15 		Clara Loeh
Universität Regensburg
Details

Geometry Seminar

Titel The spectrum of simplicial volume: groups, manifolds, and questions
Referent:in, Affiliation Clara Loeh, Universität Regensburg
Datum, Zeit 4. Mai 2022, 16:15-17:15
Ort 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. Mai 2022
16:15-17:15 		Pierre Py
Université de Strasbourg, France
Details

Geometry Seminar

Titel Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices
Referent:in, Affiliation Pierre Py, Université de Strasbourg, France
Datum, Zeit 11. Mai 2022, 16:15-17:15
Ort 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. Mai 2022
16:15-17:15 		Sahana Balasubramanya
Universität Münster
Details

Geometry Seminar

Titel Actions of solvable groups on hyperbolic spaces
Referent:in, Affiliation Sahana Balasubramanya, Universität Münster
Datum, Zeit 25. Mai 2022, 16:15-17:15
Ort 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. Juni 2022
16:15-17:15 		Thomas Haettel
University of Montpellier
Details

Geometry Seminar

Titel Group actions on injective metric spaces
Referent:in, Affiliation Thomas Haettel, University of Montpellier
Datum, Zeit 1. Juni 2022, 16:15-17:15
Ort 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

Archiv: HS 24 FS 24 HS 23 FS 23 HS 22 FS 22 HS 21 HS 20 FS 20 HS 19 FS 19 HS 18 FS 18 HS 17 FS 17 HS 16 FS 16 HS 15 FS 15 HS 14 FS 14 HS 13 FS 13 HS 12 FS 12 HS 11 FS 11 HS 10 FS 10 HS 09 FS 09

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