7 citations · 10 across the 9 of their papers we have counts for
10 papers
General Properties of the Thermo-Metric for CV event manifolds and the magnetization combinatorial scheme
Pietro Fre, Alexander S. Sorin, Mario Trigiante
Following previous results recently obtained by us, on Information Geometry versus Geometrical Thermodynamics and on the exact calculation of partition functions for extended Souri…
Thermodynamics a la Souriau on Kähler Non Compact Symmetric Spaces for Cartan Neural Networks
Pietro G. Fré, Alexander S. Sorin, Mario Trigiante
In this paper, we clarify several issues concerning the abstract geometrical formulation of thermodynamics on non compact symmetric spaces that are the mathematical…
Tessellation Groups, Harmonic Analysis on Non-compact Symmetric Spaces and the Heat Kernel in view of Cartan Convolutional Neural Networks
Pietro Fré, Federico Milanesio, Marcelo Oyarzo +2
In this paper, we continue the development of the Cartan neural networks programme, launched with three previous publications, by focusing on some mathematical foundational aspects…
Navigation through Non-Compact Symmetric Spaces: a mathematical perspective on Cartan Neural Networks
Pietro Giuseppe Fré, Federico Milanesio, Guido Sanguinetti +1
Recent work has identified non-compact symmetric spaces U/H as a promising class of homogeneous manifolds to develop a geometrically consistent theory of neural networks. An initia…
Cartan Networks: Group theoretical Hyperbolic Deep Learning
Federico Milanesio, Matteo Santoro, Pietro G. Fré +1
Hyperbolic deep learning leverages the metric properties of hyperbolic spaces to develop efficient and informative embeddings of hierarchical data. Here, we focus on the solvable g…
The paint group Tits Satake theory of hyperbolic symmetric spaces: the distance function, paint invariants and discrete subgroups
Ugo Bruzzo, Pietro Fré, Mario Trigiante
The present paper, which is partially a review, but also contains several completely new results, aims at presenting, in a unified mathematical framework, a complex and articulated…
Lectures on resolutions à la Kronheimer of orbifold singularities, McKay quivers for Gauge Theories on D3 branes, and the issue of Ricci flat metrics on the resolved three-folds
Pietro G. Fré
The present Lecture Notes have been prepared to back up a series of a few seminars given by the author at the Albert Einstein Institute in Potsdam. These Notes aim at reviewing a r…
2-branes with Arnold-Beltrami Fluxes from Minimal D=7 Supergravity
Pietro Fre, Alexander S. Sorin
We describe this paper as a Sentimental Journey from Hydrodynamics to Supergravity. Beltrami equation in three dimensions that plays a key role in the hydrodynamics of incompressib…
Classification of Arnold-Beltrami Flows and their Hidden Symmetries
Pietro Fre, Alexander S. Sorin
In the context of mathematical hydrodynamics, we consider the group theory structure which underlies the ABC-flow introduced by Beltrami, Arnold and Childress. Beltrami equation is…
The -map, Tits Satake subalgebras and the search for inflaton potentials
P. Fré, A. S. Sorin, M. Trigiante
In this paper we address the general problem of including inflationary models exhibiting Starobinsky-like potentials into (symmetric) supergravities. This is done b…