Departement Mathematik

Geometry seminar

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Herbstsemester 2021

Datum / Zeit Referent:in Titel Ort
6. Oktober 2021
15:45-16:45 		Dr. Danica Kosanović
ETH Zurich, Switzerland
Details

Geometry Seminar

Titel Light bulbs in 4-manifolds
Referent:in, Affiliation Dr. Danica Kosanović, ETH Zurich, Switzerland
Datum, Zeit 6. Oktober 2021, 15:45-16:45
Ort HG G 43
Abstract Knowing when you can embed a surface into a 4-manifold is of fundamental importance for understanding the topology of that manifold. This brave new knot theory is even harder than the classical knot theory, but in certain situations, like in the setting when your embedded surfaces have a common "light bulb", one can completely classify all of them up to isotopy. I will explain how one can use techniques from homotopy theory to do this, resulting in some surprising applications of higher homotopy groups of embedding spaces. This is joint work with Peter Teichner.
Light bulbs in 4-manifoldsread_more
HG G 43
20. Oktober 2021
15:45-16:45 		Giles Gardam
WWU Münster
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Geometry Seminar

Titel Kaplansky's conjectures
Referent:in, Affiliation Giles Gardam, WWU Münster
Datum, Zeit 20. Oktober 2021, 15:45-16:45
Ort HG G 43
Abstract Three conjectures on group rings of torsion-free groups are commonly attributed to Kaplansky, namely the unit, zero divisor and idempotent conjectures. For example, the zero divisor conjecture predicts that if K is a field and G is a torsion-free group, then the group ring K[G] has no zero divisors. I will discuss these conjectures and their relationship to other conjectures and properties of groups. I will then explain how modern solvers for Boolean satisfiability can be applied to them, producing the first counterexample to the unit conjecture.
Kaplansky's conjecturesread_more
HG G 43
27. Oktober 2021
15:45-16:45 		Arnaud Maret
Universität Heidelberg
Details

Geometry Seminar

Titel Remarkable surface group representations in genus zero
Referent:in, Affiliation Arnaud Maret, Universität Heidelberg
Datum, Zeit 27. Oktober 2021, 15:45-16:45
Ort HG G 43
Abstract This talk is about a very special kind of representations of the fundamental group of a punctured sphere into PSL(2,R), discovered by Deroin and Tholozan. These representations have the key property of being totally elliptic. We will talk about the topology of their moduli space which turns out to be compact. I will explain how to parametrize them with chains of triangles in the upper half-plane and how to extract action-angle coordinates from that polygonal model.
Remarkable surface group representations in genus zeroread_more
HG G 43
3. November 2021
15:45-16:45 		Nicolas Monod
EPF Lausanne
Details

Geometry Seminar

Titel Gelfand pairs and Iwasawa decompositions
Referent:in, Affiliation Nicolas Monod, EPF Lausanne
Datum, Zeit 3. November 2021, 15:45-16:45
Ort HG G 43
Abstract I will prove that every Gelfand pair admits an Iwasawa decomposition. Before that, I will explain what Gelfand pairs are and why Iwasawa decompositions are useful.
Gelfand pairs and Iwasawa decompositionsread_more
HG G 43
10. November 2021
15:45-16:45 		Gabriel Pallier
Sorbonne Université, France
Details

Geometry Seminar

Titel Invariants for sublinear bilipschitz equivalence
Referent:in, Affiliation Gabriel Pallier, Sorbonne Université, France
Datum, Zeit 10. November 2021, 15:45-16:45
Ort HG G 43
Abstract Sublinear bilipschitz equivalences between metric spaces are generalized quasiisometries. In this generalization, the large-scale Lipschitz behavior is kept, while the (uniformly) coarse behavior is not. These equivalences appear in the study of asymptotic cones of Lie groups by Cornulier. They occur especially between families of non-pairwise quasiisometric nilpotent or solvable connected Lie groups. In this talk, I will give an introduction to sublinear bilipschitz equivalences and report on my work on revisiting the classical quasiisometry invariants of groups to determine which of them can be turned into invariants for sublinear bilipschitz equivalence. This lies in continuation of Gromov's questions of classifying homogeneous spaces (e.g. Riemannian symmetric spaces and noncompact solvmanifolds) up to quasiisometry and investigating their quasiisometric rigidity. Finally I will present a classification result for a small family of solvable Lie groups, and discuss the partially unsolved problems of rigidity in rank one (in the appropriate sense) and classification in higher rank.
Invariants for sublinear bilipschitz equivalenceread_more
HG G 43
24. November 2021
15:45-16:45 		Hugo Parlier
University of Luxembourg
Details

Geometry Seminar

Titel Where the orthogeodesics roam
Referent:in, Affiliation Hugo Parlier, University of Luxembourg
Datum, Zeit 24. November 2021, 15:45-16:45
Ort HG G 43
Abstract The lengths of geodesics on hyperbolic surfaces satisfy intriguing equations, known as identities, relating these lengths to geometric quantities of the surface. The talk will be about a family of identities that relate lengths of closed geodesics and orthogeodesics to boundary lengths. This family includes identities due to Basmajian, McShane, Mirzakhani and Tan-Wong-Zhang as particular cases.
Where the orthogeodesics roamread_more
HG G 43

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