Chapoton F., Fauvet F., Malvenuto C., Thibon J.-Y. (eds.) Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA) Vol. 1

Paris: European Mathematical Society, 2020. — 358 p.IRMA Lectures in Mathematics and Theoretical Physics Vol. 31
This is volume 1 of a 2-volume work comprising a total of 14 refereed research articles which stem from the CARMA Conference (Algebraic Combinatorics, Resurgence, Moulds and Applications), held at the Centre International de Rencontres Mathématiques in Luminy, France, from June 26 to 30, 2017.
The conference did notably emphasise the role of Hopf algebraic techniques and related concepts (e.g. Rota–Baxter algebras, operads, Ecalle’s mould calculus) which have lately proved pervasive in combinatorics, but also in many other fields, from multiple zeta values to the algebraic study of control systems and the theory of rough paths.
The volumes should be useful to researchers or graduate students in mathematics working in these domains and to theoretical physicists involved with resurgent functions and alien calculus.
Keywords: Operad, Hopf algebra, algebraic combinatorics, moulds, renormalization, periods, multiple zeta values, resurgent functions, alien calculus, vector fields, diffeomorphismsShuffle quadri-algebras and concatenation
Structure theorems for dendriform and tridendriform algebras
A group-theoretical approach to conditionally free cumulants
The Natural Growth Scale
Realizations of Hopf algebras of graphs by alphabets
Duplicial algebras, parking functions, and Lagrange inversion
The triduplicial operad is Koszul
The Hopf algebra of integer binary relations
List of contributors