[Topology.beta] Fwd: DDT&G seminar tomorrow @Amsterdam

[Rot, T.O. (Thomas)]

Begin forwarded message:

From: "Pasquotto, F. (Federica)" <f.pasquotto at math.leidenuniv.nl>
Date: 8 May 2025 at 09:31:35 CEST
To: "Pasquotto, F. (Federica)" <f.pasquotto at math.leidenuniv.nl>
Subject: DDT&G seminar tomorrow @Amsterdam


Dear all,
This is a gentle reminder of tomorrow's Dutch Differential Topology and Geometry seminar, which will take place in Amsterdam.
Speaker:  Mario Fuentes<https://sites.google.com/view/mariofuentes> (Toulouse)
Title: What Lie algebras reveal about topological spaces
Date: Friday 9 May, 14:30-17:00
Location: Amsterdam, NU building, room 9A-46 (Maryam)

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 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 tomorrow!

Alvaro, Federica and Thomas

Abstracts

Algebraic topologists have constructed families of algebraic objects that capture the homotopical information of topological spaces, such as (co)homology groups and homotopy groups. These invariants can be refined by adding more structure, allowing them to distinguish between a broader class of spaces. Ultimately, our goal is to encode all the topological information of a space at an algebraic level.
There are several successful approaches to this task. Typically, we must impose certain conditions on the spaces (such as being connected, simply connected, nilpotent, of finite type, or rational) to apply these methods. Rational homotopy theory is one such tool: it constructs algebraic models of spaces that capture all rational information, effectively discarding the torsion part of their homotopy and homology groups. If we accept this trade-off, the resulting theory can fully encode the homotopical structure of simply-connected spaces. More formally, we establish an equivalence of homotopy categories.
Once this foundational goal is achieved, a natural direction of research is to relax some of the initial restrictions. For instance, recent advances aim to extend the theory to non-rational spaces. In this talk, we focus on removing the connectedness assumption, developing a theory for non-simply connected and even non-connected spaces. This extension relies on complete Lie algebras and introduces some technical challenges, but also opens the door to problems previously inaccessible through classical homotopy theory.

This presentation will be given in two parts. The first talk will examine the structure of homotopy and homology groups, which are of central importance in algebraic topology. We will explore their relationships and show how, by ignoring torsion, we can systematically study their algebraic structure. We will also introduce some basic aspects of Rational Homotopy Theory using differential graded Lie algebras.
In the second talk, we will delve deeper into how this approach is constructed and how it can be extended to include non-simply connected and non-connected spaces. We will present recent results in this area, along with some ongoing work in collaboration with Ricardo Campos.


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