[Topology.beta] A week of topology and a strike: CTAAAG (unusual time!!), colloquium, DDT&G.

[Rot, T.O. (Thomas)]

Dear all,

I hope to see you at the following events this week.

CTAAG on Tuesday, Colloquium on Wednesday, and DDT&G on Friday (in utrecht).

Note that the CTAAAG starts at 10:00, due to the strike

https://woinactie.blogspot.com/2025/12/programma-stakingsactie-9-december.html


CTAAAG: 10:00: homotopy theory and diffeomorphism groups

I got a blessing of Gabriele to deviate from the program. I will discuss why I care about the homotopy type of diffeomorphism groups, and I will determine the homotopy type of Diff(R^n), Diff(S^1), Diff(S^2), Diff_\partial(D^1), Diff_\partial(D^2), and comment on the higher dimensional cases. The determination of the homotopy type of S^2 is due to Smale, and as he was a dynamicist, is a dynamical systems proof. It hinges on our understanding of dynamics of the plane. As the dynamics in higher dimensions can be much more complicated, the determination of the homotopy types of higher dimensional spheres is also much more complicated.


Colloquium



Time: 10 December, 16:00

Location: Maryam: 9A-46

Speaker: Stavroula Makri (Vrije Universiteit Amsterdam)



Title: Braids and fixed points

Abstract: The use of braid group theory in surface dynamics and Nielsen fixed point theory was initiated in the early 1980s and has since played a key role in studying fixed points and periodic orbits of surface homeomorphisms. In this talk, I will begin with a basic introduction to Nielsen fixed point theory and braid group theory, and then explain how a braid can be associated with a homeomorphism of a compact surface isotopic to the identity that leaves a finite set invariant. We will see how braid theory can be applied to obtain important results and information about surface homeomorphisms. In particular, I will discuss an elegant result showing that the matrix representation of a braid provides valuable information about the existence and linking behavior of its fixed points, and how we can extend it to a 3-dimensional setting.


DDT&G

Speaker: Pedro Boavida de Brito<https://www.math.tecnico.ulisboa.pt/~pbrito/> (IST Lisbon)
Title: Smooth embeddings from the point of view of operad theory
Date: Friday 12 December, 14:30-17:00
Location: Utrecht, KBG-224

The schedule will be as follows:

2:30-3:30 p.m.: first part of the seminar (little to no prior knowledge assumed)
4:00-5:00 p.m.: second part of the seminar (slightly more advanced level)

Please notice that the first part of the seminar (2:30-3:30 p.m.) is intended for general mathematical audience, and master students with an interest in geometry and topology are especially encouraged to participate.

Please visit the seminar's webpage for additional information and an overview of past and upcoming talks:

https://www.few.vu.nl/~trt800/<https://www.few.vu.nl/~trt800/ddtg.html>ddt<https://www.few.vu.nl/~trt800/ddtg.html>g.html<https://www.few.vu.nl/~trt800/ddtg.html>

We hope to see many of you next week in Utrecht!

Alvaro, Federica and Thomas

Abstract

Given two smooth embeddings from one manifold to another, are they isotopic? In the so-called metastable range, Haefliger and Becker showed this problem is controlled by a single cohomology class, a complete obstruction to isotopy. I will explain, with examples, how embedding calculus generalises this by providing not one but a finite list of obstruction classes which form a complete obstruction to isotopy (when we have convergence).

In the second part, I will give an account of the formality of the little discs operad and describe recent joint work with Joana Cirici and Geoffroy Horel showing that formality also holds when the orthogonal group action is taken into account. This has striking consequences to the rational homotopy type of embedding spaces, which I will explain, and extends results of Fresse-Turchin-Willwacher to manifolds which are not parallelized.




Best,
Thomas


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