arXiv subjects

Y. I. Manin

Publications and source records attributed to Y. I. Manin.

3 recordsLinked to original sources

arXiv2021

Genus zero modular operad and absolute Galois group

In this article, we develop the geometry of canonical stratifications of the spaces $\mathcal{M}_{0,n}$ and prepare ground for studying the action of the Galois group $Gal (\overline{\mathbb{Q}} /\mathbb{Q})$ upon strata. We define and introduce a version of a gravity operad constructed for a class of moduli spaces $\mathcal{M}_{0,n}$, equipped with a hidden holomorphic involution. This additional symmetry is associated to a split quaternionic structure. We introduce a categorical framework to present this object. Interaction between the geometry, physics and the arithmetics are discussed. An important feature is that 0-divisors of the split quaternion algebra imply additional singular points, and lead to investigations concerning the geometry and mixed Hodge structures.

math.AG↗

arXiv2020

F-manifolds and geometry of information

The theory of $F$-manifolds, and more generally, manifolds endowed with commutative and associative multiplication of their tangent fields, was discovered and formalised in various models of quantum field theory involving algebraic and analytic geometry, at least since 1990's. The focus of this paper consists in the demonstration that various spaces of probability distributions defined and studied at least since 1960's also carry natural structures of $F$-manifolds. This fact remained somewhat hidden in various domains of the vast territory of models of information storing and transmission that are briefly surveyed here.

math.AG↗

arXiv2019

Symmetries of genus zero modular operad

In this article combining survey and certain research results, we introduce a categorical framework for description of symmetries of genus zero modular operad. This description merges the techniques of recent "persistence homology" studies and the classical formalism of groupoids. We show that the contravariant "poset in groupoids" embodying these symmetries, provides a new avatar of profinite Grothendieck-Teichmüller group acting upon this operad but seemingly not related with representations of the Galois group of all algebraic numbers.

math.AG↗