22 citations · 22 across the 16 of their papers we have counts for
7 papers · 1 filter
Shape Theory via the Atiyah--Molino Reconstruction and Deformations
Noémie C. Combe, Hanna N. Nencka
Reconstruction problems lie at the very heart of both mathematics and science, posing the enigmatic challenge: \emph{How does one resurrect a hidden structure from the shards of in…
Proving the Grothendieck--Teichmüller Conjecture for Profinite Spaces & The Galois Grothendieck Path Integral
Noémie C. Combe
We establish that the Grothendieck-Teichmuller conjecture, which predicts an isomorphism between the Grothendieck-Teichmuller group GT and the absolute Galois group of rational num…
Quantum Geometry insights in Deep Learning
Noémie C. Combe
In this paper, we explore the fundamental role of the Monge-Ampère equation in deep learning, particularly in the context of Boltzmann machines and energy-based models. We first re…
Exploring information geometry: Recent Advances and Connections to Topological Field Theory
Noémie C. Combe, Philippe G. Combe, Hanna K. Nencka
This introductory text arises from a lecture given in Göteborg, Sweden, given by the first author and is intended for undergraduate students, as well as for any mathematically incl…
On Multiquantum Bits, Segre Embeddings and Coxeter Chambers
Noémie C. Combe
This work explores the interplay between quantum information theory, algebraic geometry, and number theory, with a particular focus on multiqubit systems, their entanglement struct…
Maximum Likelihood, permutohedra and Associativity Equations
Noémie C. Combe
We consider the cone of concentration matrices related to linear concentration models and Wishart laws. We prove that this cone is a Monge--Ampère domain and that the log-likelihoo…
On the geometry of Kähler--Frobenius manifolds and their classification
Noémie. C. Combe
The purpose of this article is to show that flat compact Kähler manifolds exhibit the structure of a Frobenius manifold, a structure originating in 2D Topological Quantum Field The…