Zobrazeno 1 - 10
of 26
pro vyhledávání: '"Combe, Noemie"'
Autor:
Combe, Noemie C.
Kontsevich suggested that the Landau-Ginzburg model presents a good formalism for homological mirror symmetry. In this paper we propose to investigate the LG theory from the viewpoint of Koopman-von Neumann's construction. New advances are thus provi
Externí odkaz:
http://arxiv.org/abs/2409.00835
Autor:
Combe, Noemie C.
We prove that in any strictly convex symmetric cone $\Omega$ there exists a non empty locus where the WDVV equation is satisfied (i.e. there exists a hyperplane being a Frobenius manifold). This result holds over any real division algebra (with a res
Externí odkaz:
http://arxiv.org/abs/2309.04334
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 developed by Vinberg, Souriau and Koszul and the Frobenius manifold ap
Externí odkaz:
http://arxiv.org/abs/2201.07517
The most standard description of symmetries of a mathematical structure produces a group. However, when the definition of this structure is motivated by physics, or information theory, etc., the respective symmetry objects might become more sophistic
Externí odkaz:
http://arxiv.org/abs/2112.15237
Autor:
Combe, Noemie C.
New relations between algebraic geometry, information theory and Topological Field Theory are developed. One considers models of databases subject to noise i.e. probability distributions on finite sets, related to exponential families. We prove expli
Externí odkaz:
http://arxiv.org/abs/2110.02607
Publikováno v:
Geometric Science of Information, 2021
In this paper, we explicitly prove that statistical manifolds, related to exponential families and with flat structure connection have a Frobenius manifold structure. This latter object, at the interplay of beautiful interactions between topology and
Externí odkaz:
http://arxiv.org/abs/2107.08446
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 quantum physics, emergence of F-manifolds, and motivic enrichments.
Externí odkaz:
http://arxiv.org/abs/2107.08006
Technology of data collection and information transmission is based on various mathematical models of encoding. The words "Geometry of information" refer to such models, whereas the words "Moufang patterns" refer to various sophisticated symmetries a
Externí odkaz:
http://arxiv.org/abs/2107.07486
In this note, we sketch an approach to the problems of equivariant birational geometry developed by M. Kontsevich and Yu. Tschinkel, where Burnside invariants were introduced. We are making explicit the role of Nori constructions in this environment.
Externí odkaz:
http://arxiv.org/abs/2012.13814
A part of Grothendieck's program for studying the Galois group $G_{\mathbb Q}$ of the field of all algebraic numbers $\overline{\mathbb Q}$ emerged from his insight that one should lift its action upon $\overline{\mathbb Q}$ to the action of $G_{\mat
Externí odkaz:
http://arxiv.org/abs/2006.13663