Public Thesis defense - IRMP

SST

19 mai 2020

16h

Louvain-la-Neuve

will take place in the form of a video conference Teams

Goodwillie calculus in the category of algebras over a chain operad by Miradain ATONTSA NGUEMO

Pour l’obtention du grade de Docteur en sciences

Goodwillie functor calculus is a method invented by Thomas Goodwillie to analyze functors that arise in Topology. This theory has some compelling similarities with differential calculus of Newton and Leibnitz in the sense that the method produces a tower for approximating a functor which plays the role of the Taylor series approximating a function. One of the major difficulties in this theory is that, Goodwillie Taylor series (or towers) are very abstract from their constructions and hence not easy to compute in general.

The goal of this thesis is to produce an explicit polynomial approximation of functors between algebraic categories. Namely, we look at functors between the category of chain complexes and the category of algebras over a chain operad. We study properties on their tower of approximation, such as analyzing their homogeneous parts. These are the differences between two consecutive terms in the Taylor tower.

We get an explicit formula of homogeneous functors which is analogous to Goodwillie’s results in spaces and our result generalizes the formula of Walter who pioneered this algebraic approach. Moreover, we extend our formula on homogeneous functors to produce an explicit and computable description of the Taylor tower of arbitrary functors.

Jury members :

• Prof. Pascal Lambrechts (UCLouvain), supervisor
• Prof. Grégory Arone (Stockholm University, Sweden), supervisor
• Prof. Marino Gran (UCLouvain), chairperson
• Prof. Pedro Vaz (UCLouvain), secretary
• Prof. Benoit Fresse (Université de Lille, France)
• Dr. Pedro Boavida De Brito (Univ. of Lisbon, Portugal)

Pay attention :

The public defense of Miradain Atontsa Nguemo scheduled for Tuesday 19 May at 16:00 will indeed take place in the form of a video conference Teams.

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