Departement Mathematik

Geometry seminar

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Herbstsemester 2023

Datum / Zeit Referent:in Titel Ort
27. September 2023
15:45-16:45 		Simon Machado
EHTZ
Details

Geometry Seminar

Titel Approximate subgroups and bounded cohomology
Referent:in, Affiliation Simon Machado, EHTZ
Datum, Zeit 27. September 2023, 15:45-16:45
Ort 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. Oktober 2023
15:45-16:45 		Stefanie Zbinden
Heriot-Watt
Details

Geometry Seminar

Titel From strong contraction to hyperbolicity
Referent:in, Affiliation Stefanie Zbinden, Heriot-Watt
Datum, Zeit 25. Oktober 2023, 15:45-16:45
Ort 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
Details

Geometry Seminar

Titel A new extension of 4-dimensional mapping class groups
Referent:in, Affiliation Peter Teichner, Max Planck Institute Bonn
Datum, Zeit 1. November 2023, 15:45-16:45
Ort 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

Titel Knots in overtwisted manifolds
Referent:in, Affiliation Rima Chatterjee, University of Cologne
Datum, Zeit 22. November 2023, 15:45-16:45
Ort 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

Titel Coarse obstructions to cubulation
Referent:in, Affiliation Harry Petyt, Oxford University, UK
Datum, Zeit 29. November 2023, 15:45-16:45
Ort 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. Dezember 2023
15:45-16:45 		Geoffroy Horel
Université Paris 13
Details

Geometry Seminar

Titel Binomial rings and homotopy theory
Referent:in, Affiliation Geoffroy Horel, Université Paris 13
Datum, Zeit 6. Dezember 2023, 15:45-16:45
Ort 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. Dezember 2023
15:45-16:45 		Pedro Boavida de Brito
Instituto Superior Técnico, University of Lisbon
Details

Geometry Seminar

Titel Torus tricks and configuration spaces
Referent:in, Affiliation Pedro Boavida de Brito, Instituto Superior Técnico, University of Lisbon
Datum, Zeit 13. Dezember 2023, 15:45-16:45
Ort 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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