Séminaires de topologie algébrique

Louvain-La-Neuve

The seminar usually takes place on thursday, 11h00.

Current organisers: Miradain Atontsa Nguemo and Elia Rizzo

Past organisers: Pedro Vaz (2016-17), Federico Cantero Morán (2015-16), Pedro Boavida de Brito and Paul Arnaud Tsopméné (2014 - 2015), Urtzi Buijs Martín (2013 - 2014).

Past events: https://perso.uclouvain.be/pedro.vaz/seminar.html

 

2018/19

Oct 04        

2018

11h00-12h00   

Cyclo 07

David Méndez 

(University of Malaga)

Realising groups in arrow categories of graphs and spaces

Oct 11  

2018

11h00-12h00  

Cyclo B335

Miradain Atontsa Nguemo

UCL

Algebraic characterisation of homogeneous functors

Oct 19  

2018

11h00-12h00   

Cyclo B335

Yves Félix 

UCL

 The rational homotopy of mapping spaces - an introduction to the subject

Nov 22  

2018

11h00-12h00   

Cyclo B203-5

Federico Cantero Morán  

BGSMath

  Low-dimensional spatial refinements of Khovanov functors

 

 

Abstracts 2018/19

David Méndez (University of Malaga) , Oct 04

Title: Realising groups in arrow categories of graphs and spaces

Whenever an algebraic structure arises in any mathematical context, it is natural to ask how to characterise the algebraic objects that may appear in that context. For instance, given any category, we may ask ourselves which groups can appear as automorphism groups of objects in that category. The Kahn realisation problem goes in that direction: it asks which groups may appear as the group of self-homotopy equivalences (that is, the automorphism group in HoTop) of a space X. A partial solution was attained by Costoya-Viruel in 2014, showing that every finite group arises as self-homotopy equivalences of a space (which is in fact rational).
In this talk we consider the more general problem of realising groups in arrow categories of a given category C, Arr(C). In Arr(C), objects are arrows in C and morphisms between two arrows are commutative squares, thus given by two arrows in C. In this context, we ask: Given G1, G2 groups and H a subgroup of G1xG2, is there an arrow f:X1--->X2 in C such that Aut(Xi)=Gi and Aut(f)=H? We build a solution in the category of Graphs and show how to translate it to spaces, by means of algebraic models of rational homotopy types of spaces.
Miradain Atontsa Nguemo (UCL) , Oct 11

Title: Algebraic characterization of homogeneous functors

Goodwillie developped, in a serie of papers in 1990, 1992 and 2003, an approach to give polynomial approximations of functors F: Top ----> Top. In the Taylor tower that he has constructed: 
              F ... ----->P_nF -----> P_n-1 F ------> .... ------> P_1F 
he was able to characterize explicitely the homotopy fibres D_nF of the maps in the tower. 
In this talk, I will give an overall idea of the Goodwillie approximation for functors F: C ----> D, when C and D are any of the model categories: "Chain complexes", "DGL=differential graded Lie algebras", "Alg_O=Algebras over the operad O". I will end by giving the characterization of homogeneous functors from C to D.
Yves Félix (UCL) , Oct 19

Title : The rational homotopy of mapping spaces - an introduction to the subject 

We will begin with a description of the approaches of Haefliger and Brown-Szczarba, and ends with a presentation of Lie models in the spirit of Lazarev-Markl, Getzler and Berglund)