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Autumn Semester 2023

Date / Time Speaker Title Location
27 September 2023
15:45-16:45 		Simon Machado
EHTZ
Details

Geometry Seminar

Title Approximate subgroups and bounded cohomology
Speaker, Affiliation Simon Machado, EHTZ
Date, Time 27 September 2023, 15:45-16:45
Location HG G 43
Abstract Approximate subgroups are subsets of groups that are stable under multiplication up to a finite multiplicative error. The study of approximate subgroups has long been motivated by problems regarding random walks, expansion and growth in groups. A notion of regularity - coined laminarity - has plaid a crucial role in the understanding of their structure. In a recent breakthrough, Hrushovski noticed that failure of laminarity could be witnessed by a certain bounded cohomology class. I will explain why another notion of cohomology - that sits halfway between bounded cohomology and group cohomology - is more suitable. I will then discuss how this can be used to classify approximate lattices - a class of approximate subgroups first studied by Yves Meyer that generalises at the same time lattices of locally compact groups, Pisot numbers of a number field and Penrose tilings.
Approximate subgroups and bounded cohomologyread_more
HG G 43
25 October 2023
15:45-16:45 		Stefanie Zbinden
Heriot-Watt
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Geometry Seminar

Title From strong contraction to hyperbolicity
Speaker, Affiliation Stefanie Zbinden, Heriot-Watt
Date, Time 25 October 2023, 15:45-16:45
Location HG G 43
Abstract For almost 10 years, it has been known that if a group contains a strongly contracting element, then it is acylindrically hyperbolic. Moreover, one can use the Projection Complex of Bestvina, Bromberg and Fujiwara to construct a hyperbolic space where said element acts WPD. For a long time, the following question remained unanswered: if Morse is equivalent to strongly contracting, does there exist a space where all generalized loxodromics act WPD? In this talk, I will present a construction of a hyperbolic space, that answers this question positively.
From strong contraction to hyperbolicity read_more
HG G 43
1 November 2023
15:45-16:45 		Peter Teichner
Max Planck Institute Bonn
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Geometry Seminar

Title A new extension of 4-dimensional mapping class groups
Speaker, Affiliation Peter Teichner, Max Planck Institute Bonn
Date, Time 1 November 2023, 15:45-16:45
Location HG G 43
A new extension of 4-dimensional mapping class groups
HG G 43
22 November 2023
15:45-16:45 		Rima Chatterjee
University of Cologne
Details

Geometry Seminar

Title Knots in overtwisted manifolds
Speaker, Affiliation Rima Chatterjee, University of Cologne
Date, Time 22 November 2023, 15:45-16:45
Location HG G 43
Abstract Knots in contact manifolds are interesting objects to study. Contact structures come in two flavors- tight and overtwisted. In this talk, I'll focus on knots in overtwisted manifolds. The knots that we really care about in this setting are known as non-loose or exceptional knots. I'll define what these knots are and then mention some of their existence and classification results. If time permits, I'll talk about how one can contruct a family of non-loose knots via cabling. This is based on joint work with Etnyre, Min and Mukherjee. No background knowledge of contact topology will be assumed.
Knots in overtwisted manifoldsread_more
HG G 43
29 November 2023
15:45-16:45 		Harry Petyt
Oxford University, UK
Details

Geometry Seminar

Title Coarse obstructions to cubulation
Speaker, Affiliation Harry Petyt, Oxford University, UK
Date, Time 29 November 2023, 15:45-16:45
Location HG G 43
Abstract Given a group G, finding a geometric action of G on a CAT(0) cube complex can be used to say some rather strong things about G. Such actions are not always easy to find, however, which makes it useful to have sufficient conditions, both for existence and for non-existence. This talk concerns the latter: we shall see a coarse geometric obstruction to a group admitting a cocompact cubulation. Based on joint work with Zach Munro.
Coarse obstructions to cubulationread_more
HG G 43
6 December 2023
15:45-16:45 		Geoffroy Horel
Université Paris 13
Details

Geometry Seminar

Title Binomial rings and homotopy theory
Speaker, Affiliation Geoffroy Horel, Université Paris 13
Date, Time 6 December 2023, 15:45-16:45
Location HG G 43
Abstract A fundamental question in algebraic topology is the following: how much information on a space can be deduced from its cohomology. There is of course no hope to get more than the underlying homotopy type of the space. On the other hand, Sullivan has famously proved that the rational homotopy type of a space is determined by the algebra of rational cochains (in particular rationalized homotopy groups can be computed from this data). My goal in this talk is to explain an integral lift of this theorem based on the theory of binomial rings.
Binomial rings and homotopy theoryread_more
HG G 43
13 December 2023
15:45-16:45 		Pedro Boavida de Brito
Instituto Superior Técnico, University of Lisbon
Details

Geometry Seminar

Title Torus tricks and configuration spaces
Speaker, Affiliation Pedro Boavida de Brito, Instituto Superior Técnico, University of Lisbon
Date, Time 13 December 2023, 15:45-16:45
Location HG G 43
Abstract Given a topological embedding (i.e. injective continuous map), evaluation on finite subsets defines a map between configuration spaces which is coherent as we vary cardinalities. It turns out that, if the codimension is at least three, no homotopically information is lost in this process. This is in stark contrast to the situation in codimension zero, as shown by Krannich-Kupers. I will discuss some constructions and ideas involved in showing the high-codimension result, notably, a configuration space version of a torus trick from classical geometric topology. This is joint work with Michael Weiss.
Torus tricks and configuration spacesread_more
HG G 43

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