Zobrazeno 1 - 10
of 331
pro vyhledávání: '"Combe N."'
Autor:
Combe, N. C.
This article develops, via the perspective of (arithmetic) algebraic geometry and category theory, different aspects of geometry of information. First, we describe in the terms of Eilenberg--Moore algebras over a Giry monad, the collection $Cap_n$ of
Externí odkaz:
http://arxiv.org/abs/2212.09138
Autor:
Combe, N. C., Kalugin, A.
We consider the Grothendieck--Teichm\"uller group under a new aspect. Using real algebraic geometry and web theory we show that it preserves dihedral symmetry relations, present in the fundamental groupoids of configuration spaces of marked points on
Externí odkaz:
http://arxiv.org/abs/2209.00966
In a recent paper, we described a lifting of coordinate rings of groups, loops, quantum groups, etc. to the categoric setup of operads. In most examples of that paper, these rings are non--commutative. Quantum physics of the XX--th century added one
Externí odkaz:
http://arxiv.org/abs/2208.11629
Publikováno v:
In Computational Materials Science 5 February 2025 249
Recently, it has been shown that the statistical manifold, related to exponential families, has a Frobenius manifold structure and appears as the fourth class of Frobenius manifolds. It has a structure of a projective manifold over a rank two Frobeni
Externí odkaz:
http://arxiv.org/abs/2109.13605
The recently discovered fourth class of Frobenius manifolds by Combe--Manin in opened and highlighted new geometric domains to explore. The guiding mantra of this article is to show the existence of hidden geometric aspects of the fourth Frobenius ma
Externí odkaz:
http://arxiv.org/abs/2107.01985
Autor:
Combe, N. C.
The configuration space of $n$ marked points on the complex plane is considered. We investigate a decomposition of this space by so-called Gauss-skizze i.e. a class of graphs being forests, introduced by Gauss. It is proved that this decomposition is
Externí odkaz:
http://arxiv.org/abs/2007.01604
Autor:
Combe, N. C., Manin, Y. I.
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 geome
Externí odkaz:
http://arxiv.org/abs/2004.08808
Autor:
Combe, N. C., Manin, Y. I.
Publikováno v:
Integrability, Quantization, and Geometry, Vol. II., AMS Proceedings of Symposia in Pure Mathematics, 2021
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 cl
Externí odkaz:
http://arxiv.org/abs/1907.10317
Autor:
Combe, N. C., Manin, Y. I.
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 ve
Externí odkaz:
http://arxiv.org/abs/1907.10313