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Spring Semester 2023

Date / Time Speaker Title Location
1 March 2023
15:45-16:45 		Jérémy Blanc
Universität Basel
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Geometry Seminar

Title Quotients of Cremona groups
Speaker, Affiliation Jérémy Blanc, Universität Basel
Date, Time 1 March 2023, 15:45-16:45
Location HG G 43
Abstract For n>=1, the Cremona group is the group of birational transformations of the projective space of dimension n. Algebraically, it is the Galois group of a purely transcendental extension. I will present the group and speak about the following question: which groups are quotients of this groups? I will try to present in a geometric way the answer to this question, that is very different in dimension 1,2,3 and 4.
Quotients of Cremona groupsread_more
HG G 43
8 March 2023
15:45-16:45 		Laura Ciobanu
Heriot-Watt University
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Geometry Seminar

Title Diophantine Problems in groups
Speaker, Affiliation Laura Ciobanu, Heriot-Watt University
Date, Time 8 March 2023, 15:45-16:45
Location HG G 43
Abstract For a group or semigroup or ring G, solving equations where the coefficients are elements in G and the solutions take values in G can be seen as akin to solving systems of linear equations in linear algebra, Diophantine equations in number theory, or more generally polynomial systems in algebraic geometry. Inspired by number theory, the collection of questions surrounding the solvability of equations and the description of their solutions is often referred to as `Diophantine Problems in groups’. In this talk I will give a survey about solving equations in infinite non-abelian groups, with emphasis on the hyperbolic ones, and extensions thereof.
Diophantine Problems in groupsread_more
HG G 43
15 March 2023
15:45-16:45 		Alejandra Garrido
Universidad Autónoma de Madrid
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Geometry Seminar

Title Detecting free factors in profinite completions
Speaker, Affiliation Alejandra Garrido, Universidad Autónoma de Madrid
Date, Time 15 March 2023, 15:45-16:45
Location HG G 43
Abstract If one is interested in finitely generated residually finite groups, it is natural to ask to what extent such a group is determined by all its finite quotients. The finite quotients of a group are encoded in the group's profinite completion. Perhaps the boldest question in this area is that attributed to Remeslennikov: "If G has the same profinite completion as a free group of finite rank, must G be isomorphic to that free group?" The answer to this still seems remote, given current knowledge, but some success has been found on variants of it, restricting the type of group G is allowed to be. Another natural variant of Remeslennikov's question is whether a free factor of a group G can be detected from its profinite completion: if G has a subgroup H, whose closure in the profinite completion of G is a profinite free factor, must H be a free factor of G? This question is still hard, with positive known answer only when G itself is a free group. I will report on joint work with A. Jaikin in which we provide a new proof of the above positive answer and extend it to the case when G is virtually free. The methods may be extended to other classes of groups if some interesting questions are answered on their completed group algebras. No knowledge of profinite groups will be assumed for the talk.
Detecting free factors in profinite completionsread_more
HG G 43
22 March 2023
15:45-16:45 		Conchita Martínez Pérez
Universidad de Zaragoza
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Geometry Seminar

Title Sigma invariants of some Artin groups
Speaker, Affiliation Conchita Martínez Pérez, Universidad de Zaragoza
Date, Time 22 March 2023, 15:45-16:45
Location HG G 43
Abstract Sigma invariants are geometric invariants associated to a finitely generated group that can be used to determine the homological and homotopical finiteness properties of coabelian subgroups. The Sigma invariants for right angled Artin groups have been computed by Meier, Meinert and VanWyck. In this talk we will see how to generalize their computations to some Artin groups. This is a joint work with Ruben Blasco, José Ignacio Cogolludo and Marcos Escartín.
Sigma invariants of some Artin groupsread_more
HG G 43
29 March 2023
15:45-16:45 		Alina Vdovina
Newcastle University
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Geometry Seminar

Title Higher-dimensional automata, Ramanujan shifts and buildings
Speaker, Affiliation Alina Vdovina, Newcastle University
Date, Time 29 March 2023, 15:45-16:45
Location HG G 43
Abstract We suggest a new definition of higher-dimensional automata motivated by cocompact quotients of buildings. We construct infinite series of such automata and produce very explicit constructions of Ramanujan higher-dimensional graphs.
Higher-dimensional automata, Ramanujan shifts and buildingsread_more
HG G 43
5 April 2023
15:45-16:45 		Henry Bradford
University of Cambridge
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Geometry Seminar

Title Identities with constants for finite groups
Speaker, Affiliation Henry Bradford, University of Cambridge
Date, Time 5 April 2023, 15:45-16:45
Location HG G 43
Abstract An identity, or law, for a group G is a nontrivial equation in one or more variables, which is always satisfied when the variables are evaluated in G. Every finite group satisfies a law, and it is natural to ask for the length of the shortest law for G, and to investigate how this length reflects the structure of G. These questions are explored in several papers in the literature. In ongoing joint work with Jakob Schneider and Andreas Thom, we investigate how the answers to these questions may change (or not) when our equations are allowed to contain constants in G as well as variables.
Identities with constants for finite groupsread_more
HG G 43
19 April 2023
15:45-16:45 		Michael Borinsky
ITS
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Geometry Seminar

Title On the amount of top-weight cohomology in the moduli space of curves
Speaker, Affiliation Michael Borinsky, ITS
Date, Time 19 April 2023, 15:45-16:45
Location HG G 43
Abstract I will present new results on the asymptotic growth rate of the Euler characteristic of Kontsevich's commutative graph complex. By a work of Chan, Galatius and Payne, these results imply the same asymptotic growth rate for the top-weight Euler characteristic of M_g, the moduli space of curves, and establish the existence of large amounts of unexplained top-weight cohomology in this space. I will illustrate the ingredients for the proof and comment on related recent work with Karen Vogtmann on Out(F_n) and the moduli space of graphs.
On the amount of top-weight cohomology in the moduli space of curvesread_more
HG G 43
26 April 2023
15:45-16:45 		Yuri Santos Rego
University of Magdeburg
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Geometry Seminar

Title Classical arithmetic groups and their (rational) cohomology
Speaker, Affiliation Yuri Santos Rego, University of Magdeburg
Date, Time 26 April 2023, 15:45-16:45
Location HG G 43
Abstract Cohomological information about arithmetic groups is of great interest to algebraists, geometers, and number theorists alike. In this talk we will review some important cohomological properties of (S-)arithmetic groups, looking at concrete examples and some famous results. Among these is a thorem of Lee--Szczarba, stating that the cohomology of SL(n,Z) with rational coefficients is zero in dimension n(n-1)/2. Shifting focus to arithmetic subgroups of classical semisimple groups, we shall see how to obtain --- with the aid of Coxeter groups and buildings --- a generalization of the theorem of Lee--Szczarba: the rational cohomology of such arithmetic groups vanishes in their virtual cohomological dimension. Based on joint work with B. Brück and R. Sroka.
Classical arithmetic groups and their (rational) cohomologyread_more
HG G 43
3 May 2023
15:45-16:45 		Nicola Cavallucci
KIT
Details

Geometry Seminar

Title Convergence and collapse of CAT(0)-spaces and groups
Speaker, Affiliation Nicola Cavallucci, KIT
Date, Time 3 May 2023, 15:45-16:45
Location HG G 43
Abstract I will present the possible Gromov-Hausdorff limits of geodesically complete, CAT(0)-spaces admitting a discrete group of isometries of bounded codiameter and the structure of the possible limit groups. The focus will be on the collapsing case: namely when the injectivity radius of the quotient space goes to zero along the sequence. Joint work with A.Sambusetti.
Convergence and collapse of CAT(0)-spaces and groupsread_more
HG G 43
10 May 2023
15:45-16:45 		Dr. Daniele Semola
ETH Zurich, Switzerland
Details

Geometry Seminar

Title Fundamental Groups and the Milnor Conjecture
Speaker, Affiliation Dr. Daniele Semola, ETH Zurich, Switzerland
Date, Time 10 May 2023, 15:45-16:45
Location HG G 43
Abstract It was conjectured by John Milnor in 1968 that the fundamental group of a complete Riemannian manifold with non negative Ricci Curvature is finitely generated. I will present recent joint work with Elia Bruè and Aaron Naber where we construct a complete 7-dimensional Riemannian manifold with nonnegative Ricci Curvature and infinitely generated fundamental group, thus providing a counterexample to the Milnor conjecture.
Fundamental Groups and the Milnor Conjectureread_more
HG G 43
24 May 2023
15:45-16:45 		Marco Moraschini
University of Bologna
Details

Geometry Seminar

Title Simplicial volume and aspherical manifolds
Speaker, Affiliation Marco Moraschini, University of Bologna
Date, Time 24 May 2023, 15:45-16:45
Location HG G 43
Abstract Simplicial volume is a homotopy invariant for compact manifolds introduced by Gromov that measures the complexity of a manifold in terms of singular simplices. A celebrated question by Gromov (~’90) asks whether all oriented closed connected aspherical manifolds with zero simplicial volume also have vanishing Euler characteristic. In this talk, we will describe the problem and we will show counterexamples to some variations of the previous question. Moreover, we will describe some new strategies to approach the problem as well as the relation between Gromov’s question and other classical problems in topology. This is part of a joint work with Clara Löh and George Raptis.
Simplicial volume and aspherical manifoldsread_more
HG G 43
31 May 2023
15:45-16:45 		Gonzalo Ruiz Stolowicz
EPF Lausanne
Details

Geometry Seminar

Title Hyperbolic representations of SL_2(R)
Speaker, Affiliation Gonzalo Ruiz Stolowicz, EPF Lausanne
Date, Time 31 May 2023, 15:45-16:45
Location HG G 43
Abstract We will briefly review the representations of groups in infinite-dimensional hyperbolic spaces. In particular, the family of SL2(R) representations will be studied, an operation on them that resembles a convex combination will be introduced and a partial classification will be presented.
Hyperbolic representations of SL_2(R)read_more
HG G 43

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