[Topology.beta] AG tomorrow

[Rot, T.O. (Thomas)]

Dear all,

Fabio was planned to speak tomorrow in the AG. He just emailed me that he has fallen ill unfortunately. I decided to step in, but I don’t have too much time to prepare. Prepare for that.

05-03-2024 11:00 in Maryam (NU9A46): Thomas: I like big balls and I cannot lie

Abstract: I will talk about the topology of infinite dimensional manifolds. For half an hour or so I will discuss a result Lauran and I obtained last summer on infinite dimensional homotopy groups. For the rest I will speak about  ongoing work with Alberto Abbondandolo, Lauran and Michael on questionable homology. I will talk about some true statements that we can prove, and discuss some conjectures.

The two weeks after we have external speakers: A guest of mine, and a guest of Senja. It would be nice to draw a crowd.

AG: 12-03-2024: 11:00 in Maryam: Karandeep Singh (Bonn) : Stability problems and differential graded Lie algebras

Abstract: Stability problems appear in various forms throughout geometry and algebra. For example, given a vector field $X$ on a manifold that vanishes in a point, when do all nearby vector fields also vanish somewhere? As an example in algebra, we can consider the following question: Given a Lie algebra $\mathfrak g$, and a Lie subalgebra $\mathfrak h$, when do all deformations of the Lie algebra structure on $\mathfrak g$ admit a Lie subalgebra close to $\mathfrak h$? I will show that both questions are instances of a general question about differential graded Lie algebras, and under a finite-dimensionality condition which is satisfied in the situations above, I will give a sufficient condition for a positive answer to the general question. I will then discuss the application to fixed points of Lie algebra actions.



AG: 19-03-2024: 11:00 in Maryam: Yuka Kotorii <https://wpi-skcm2.hiroshima-u.ac.jp/people/yuka-kotorii/> (Hiroshima): Homotopy theories of colored links and spatial graphs

Abstract: Two links are called link-homotopic if they are transformed to each other by a sequence of self-crossing changes and ambient isotopies. The notion of link-homotopy is generalized to spatial graphs and it is called component-homotopy. The link-homotopy classes were classified by Habegger and Lin through the classification of the link-homotopy classes of string links. In this talk, we classify colored string links up to colored link-homotopy by using the Habegger-Lin theory. Moreover, we classify colored links and spatial graphs up to colored link-homotopy and component-homotopy respectively. This research is joint work with Atsuhiko Mizusawa.

Best,
Thomas
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