12 citations · 22 across the 18 of their papers we have counts for
19 papers
Hidden symmetries of the Grothendieck--Teichmüller group
N. C. Combe, A. Kalugin
We consider the Grothendieck--Teichmüller group under a new aspect. Using real algebraic geometry and web theory we show that it preserves dihedral symmetry relations, present in t…
Quantum SUSY operads
N. C. Combe, Yu. I. Manin, M. Marcolli
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…
Symplectic and Poisson geometry of the information geometry's Frobenius manifold
Noemie Combe, Philippe Combe, Hanna Nencka
We prove that the information geometry's Frobenius manifold is a symplectic manifold having Poisson structures. By proving this statement, a bridge is created between the theories…
A note on exponential varieties, statistical manifolds and Frobenius structures
Noemie C. Combe
New relations between algebraic geometry, information theory and Topological Field Theory are developed. One considers models of databases subject to noise i.e. probability distrib…
Algebraic properties of the information geometry's fourth Frobenius manifold
N. C. Combe, P. G. Combe, H. K. Nencka
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 manifold…
Geometry of Information: classical and quantum aspects
Noemie Combe, Yuri I. Manin, Matilde Marcolli
In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and…