Graded algebras and the Lagrange inversion formula

Plática dada por Vladimir Dotsenko (Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional,CINVESTAV & Trinity College Dublín) en el evento Graded Algebras, Geometry and related Topics para celebrar el 60 aniversario de Adolfo Sánchez Valenzuela el jueves 17 de noviembre del 2016 en la Universidad Autónoma de Yucatán (UADY)

Abstract:
In 1960s, Jim Stasheff defined associahedra, remarkable CW-complexes that can encode a homotopically coherent notion of asso-ciativity. They have been realised as polytopes with integer coordinates inseveral diferent ways over the past few decades. I shall explain that therealisations of associahedra due to Loday lead to toric varieties of particu-lar merit. These varieties have been already studied by Escobar under thename “brick manifolds”, in the context of subword complexes for Coxetergroups. It turns out that they also arise as “wonderful models” in the senseof de Concini and Procesi for certain subspace arrangements. Guided bythat geometric picture, I shall argue that in some sense these varieties give a “noncommutative version” of Deligne-Mumford compactifications of modulispaces of genus zero curves with marked points, in particular they give riseto remarkable algebraic structures resembling cohomological eld theories ofKontsevich and Manin. This is a joint work with Sergey Shadrin and BrunoVallette.

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