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RTG Lecture “Asymptotic Invariants and Limits of Groups and Spaces” (Sommersemester 2019)

Vorlesung: Dienstag 9:45-13:00 SR 2.58
Dienstag 15:00-16:30 SR 1.067
Dozent Prof. Dr. Roman Sauer
Sprechstunde: nach Vereinbarung
Zimmer 1.001 Kollegiengebäude Mathematik (20.30)
Email: roman.sauer@kit.edu
Dozent Prof. Dr. Wilderich Tuschmann (Sprecher des Institutes)
Sprechstunde: derzeit nur nach vorheriger Vereinbarung per E-Mail
Zimmer 1.002 Kollegiengebäude Mathematik (20.30)
Email: tuschmann@kit.edu

This semester’s RTG lecture will be split between courses by Urs Fuchs on “Gromov's nonsqueezing theorem” and by Jonas Beyrer on “CAT(0) cube complexes and applications to group theory and low-dimensional topology”.

Gromov's nonsqueezing theorem (Urs Fuchs)

Abstract: A basic challenge in symplectic geometry is to discern rigid and flexible phenomena on symplectic manifolds. One of the first manifestations of rigidity in symplectic geometry is Gromov's nonsqueezing theorem. In these lectures I will give some background for this result and then discuss some techniques (in particular the study of holomorphic curves in symplectic manifolds) which can be used to establish such a rigidity result.

CAT(0) cube complexes and applications to group theory and low-dimensional topology (Jonas Beyrer)

Abstract: In the last 20 years CAT(0) cube complexes became an important tool to address problems in group theory and related areas, such as low-dimensional topology. On one hand this comes form the fact that many groups act ‘nicely’ on those spaces and on the other hand such actions allow to derive strong algebraic properties of the group.

In this lecture we want to develop the theory of CAT(0) cube complexes and some of their applications. More precisely: We motivate the subject with group actions on trees and group splittings. We then develop the theory of CAT(0) cube complexes and properties of groups acting on them. Finally, we consider 'special' cube complexes and their crucial role in 'recent' proofs of old conjectures about 3-manifolds.