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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">Dear all,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">Next week two nice topology events. Riya is speaking in the CTAAAG.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">Friday we have a DDT&G at the VU. Details below.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">Best,<br>
Thomas<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">You are cordially invited to attend the next Dutch Differential Topology and Geometry seminar, which will take place next week in Amsterdam. <o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><b><span style="color:black">Speaker</span></b><span style="color:black">: Mario Fuentes (Toulouse)<o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="color:black">Title</span></b><span style="color:black">: What Lie algebras reveal about topological spaces<o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="color:black">Date</span></b><span style="color:black">: Friday 9 May, 14:30-17:00<o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="color:black">Location</span></b><span style="color:black">: Amsterdam, NU building, room 9A-46 (Maryam)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">The schedule will be as follows:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black">2:30-3:30 p.m.: first part of the seminar (little to no prior knowledge assumed)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black">4:00-5:00 p.m.: second part of the seminar (slightly more advanced level)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">Please visit the seminar's webpage for additional information and an overview of past and upcoming talks:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><br>
</span><u><span style="color:blue"><a href="https://www.few.vu.nl/~trt800/ddtg.html" target="_blank" title="Original URL: https://www.few.vu.nl/~trt800/ddtg.html. Click or tap if you trust this link.">https://www.few.vu.nl/~trt800/</a></span></u><u><span style="color:#070706"><a href="https://www.few.vu.nl/~trt800/ddtg.html" target="_blank" title="Original URL: https://www.few.vu.nl/~trt800/ddtg.html. Click or tap if you trust this link."><span style="color:#070706">ddt</span></a></span></u><u><span style="color:blue"><a href="https://www.few.vu.nl/~trt800/ddtg.html" target="_blank" title="Original URL: https://www.few.vu.nl/~trt800/ddtg.html. Click or tap if you trust this link.">g.html</a></span></u><o:p></o:p></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">We hope to see many of you next week!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">Alvaro, Federica and Thomas<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="color:black">Abstract</span></b><span style="color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><span style="color:black">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.<br>
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. <br>
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. <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black">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. <br>
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.<o:p></o:p></span></p>
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