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Combinatorics and algebra of partially ordered sets - lecture 1

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Virtualconference
Authors : Chapoton, Frédéric (Author of the conference)
CIRM (Publisher )

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Abstract : Algebraic combinatorics studies combinatorial objects with an algebraic point of view, and conversely. As such, it is also a very fertile ground for experimental mathematics, involving both classical and new algorithms. I will discuss two topics: finite partially ordered sets and their invariants, and tree-indexed polynomials and power series. Finite partially ordered sets are discrete objects, that can be seen as directed graphs, but also possess an interesting representation theory. This leads to many difficult questions about a subtle equivalence relation, namely posets having equivalent derived categories. The theme of tree-indexed series, which can be traced back to Cayley, plays a role in the study of vector fields and ordinary differential equations. It is nowadays better understood in the framework of operads and can be considered as a nonassociative version of the study of alphabets, words and languages. Surprisingly maybe, rooted trees also appear in the study of iterated integrals, stemming out of the usual "integration-by-part" rule. I will describe the corresponding notions of algebras, without diving too much into the theory of operads. On the way, I will discuss some of the involved algorithms and their implementations.

Keywords : poset; incidence algebra; Coxeter polynomial; pre-Lie algebra; shuffle algebras

MSC Codes :
06A06 - Partial order, general
16G20 - Representations of quivers and partially ordered sets
17A30 - Algebras satisfying other identities
18G80 - Derived categories, triangulated categories

Additional resources :
https://www.cirm-math.fr/RepOrga/2564/Slides/1_slides_posets_chapoton.pdf

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : French
    Available date : 19/03/2021
    Conference Date : 01/03/2021
    Subseries : Research School
    arXiv category : Combinatorics ; Representation Theory
    Mathematical Area(s) : Algebra ; Combinatorics
    Format : MP4 (.mp4) - HD
    Video Time : 01:35:42
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2021-03-03_Chapoton_1.mp4

Information on the Event

Event Title : French Computer Algebra Days / JNCF - Journées nationales de calcul formel
Event Organizers : Bardet, Magali ; Busé, Laurent ; Koseleff, Pierre-Vincent ; Vaccon, Tristan
Dates : 01/03/2021 - 05/03/2021
Event Year : 2021
Event URL : https://conferences.cirm-math.fr/2564.html

Citation Data

DOI : 10.24350/CIRM.V.19718803
Cite this video as: Chapoton, Frédéric (2021). Combinatorics and algebra of partially ordered sets - lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19718803
URI : http://dx.doi.org/10.24350/CIRM.V.19718803

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