[Topology.beta] DDT&G: Pedro Boavida de Brito Smooth embeddings from the point of view of operad theory

[Benedetti, G. (Gabriele)]

Hi all,

With Stavroula we are meeting at 11:15 in the living room of the math department of the VU to take a train at 11:42 from Amsterdam Zuid.

If you want to join us, write me a message.

Lots of hugs and operads,

Gabriele

From: _list_topology.beta-bounces <topology.beta-bounces at listserver.vu.nl> On Behalf Of Rot, T.O. (Thomas)
Sent: Thursday, 11 December 2025 18:59
To: _list_topology.beta <topology.beta at listserver.vu.nl>
Subject: [Topology.beta] DDT&G: Pedro Boavida de Brito Smooth embeddings from the point of view of operad theory

Dear all,

Below is the announcement for the DDT&G tomorrow.

Some practicalities: We'll have lunch at the Educatorium at 12:30

https://www.uu.nl/en/educatorium

Gabriele is organizing a group to leave from the department in the morning.

See you there!

Best,
Thomas



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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