# Alessandro Oneto

(he/his)### Associate Professor @ Università di Trento (Italy)

email: name . surname @ unitn . it

### Short Bio

I obtained my Ph.D. in Mathematics in June 2016 at Stockholm University (Sweden) with a thesis with title Waring-type problems for polynomials in algebraic geometry, under the supervision of Boris Shapiro and Enrico Carlini.

After my graduation, I have been from November 2016 to December 2017 a Postdoctoral Researcher at Inria Sophia Antipolis Méditerranée (France) in the team Aromath, supervised by Bernard Mourrain. Between January 2018 and March 2019, I was a Postdoctoral Fellow of the Barcelona Graduate School of Mathematics (BGSMath) in Barcelona (Spain) and I was part of the group of Marta Casanellas at Universitat Politècnica de Catalunya. From April 2019 to March 2020, I was a Postdoctoral Fellow of the Alexander von Humboldt Foundation (Germany) and I was part of the group of Thomas Kahle at OvGU Magdeburg.

In April 2020, I joined the Università di Trento (Italy) as an tenure-track Assistant Professor (Ricercatore RTD-b). Since April 2023, I am an Associate Professor.

Here you can find my complete CV.

### Research interests

My research interests are mostly in Commutative Algebra and Algebraic Geometry. I like to study geometric models that have relations to problems coming from applied sciences as the study of tensor decompositions or algebraic statistical models coming from phylogenetics or machine learning. These involve the study of Hilbert functions of 0-dimensional schemes secant varieties of classical projective varieties as Veronese, Segre and Segre-Veronese varieties, apolarity theory and Macaulay inverse systems.

Here is the full list of my research works.

Here is a selected list of slides from presentations.

### Where I will be

Rigidity in Action

Workshop #3 of semester on "Rigidity and Flexibility"

RICAM, Linz (Austria), 8-12 April 2024

Tensors Algebra-Geometry-Applications

Pingree Park, Fort Collins U. (USA), June 3-7

MEGA 2024

MPI MiS Leipzig (Germany), July 29-August 2

BM60

Workshop for Bernard Mourrain's 60th birthday

MPI MiS Leipzig (Germany), August 3

### New preprints

### Hadamard-Hitchcock Decompositions: identifiability and computation

joint work with N. Vannieuwenhoven (KU Leuven)

joint work with N. Vannieuwenhoven (KU Leuven)

A Hadamard–Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as a Hadamard product of several tensor rank decompositions. Such decompositions can encode probability distributions that arise from statistical graphical models associated to complete bipartite graphs with one layer of observed random variables and one layer of hidden ones, usually called restricted Boltzmann machines. We establish generic identifiability of Hadamard–Hitchcock decompositions by exploiting the reshaped Kruskal criterion for tensor rank decompositions. A flexible algorithm leveraging existing decomposition algorithms for tensor rank decomposition is introduced for computing a Hadamard-Hitchcock decomposition. Numerical experiments illustrate its computational performance and numerical accuracy.

### On schemes evinced by Generalized Additive Decompositions and their regularity

joint work with A. Bernardi (U. Trento) and D. Taufer (KU Leuven)

joint work with A. Bernardi (U. Trento) and D. Taufer (KU Leuven)

We define and explicitly construct schemes evinced by generalized additive decompositions (GADs) of a given d-homogeneous polynomial F. We employ GADs to investigate the regularity of 0-dimensional schemes apolar to F, focusing on those satisfying some minimality conditions. We show that irredundant schemes to F need not be d-regular, unless they are evinced by special GADs of F. Instead, we prove that tangential decompositions of minimal length are always d-regular, as well as irredundant apolar schemes of length at most 2d + 1.

Within the Department of Mathematics of the U. of Trento, we created the TensorDec Laboratory. The lab wants to be a recipient of activities, both research and formation. It aims to connect master and graduate students to the different aspects of the topic of tensor decompositions:

great literature in pure algebra and geometry has been dedicated to problems inspired by questions on tensor decompositions;

the practical search for decompositions of given tensors presents very challenging computational problems which require tools from computational mathematics and complexity theory;

often data are stored in the form of tensors and, therefore, the study of tensor decompositions has a very wide spectrum of applications in real-world problems.

PhD positions @ TensorDec Lab

The TensorDec Laboratory will be part of the Marie Skłodowska-Curie Doctoral Network TENORS

The network will run from 2024 to 2027. It will be coordinated by Bernard Mourrain (Inria Sophia Antipolis, France) and with partners in France, the Netherlands, Germany, Norway, Italy, Czech Republic and Spain. In the network there will be 15 PhD position starting on October 2024.

If you are interested, or you know someone who might be, let us know!

The lab is a joint project between the Department of Mathematics and the Department of Humanities and Philosophy and it is devoted to the communication of mathematics, with a special emphasis on historical and philosophical aspects. The aim of the Lab is to provide an institutional framework to the various activities concerning the popularisation, history, and philosophy of mathematics jointly organised by the two departments over the last few years.

I agree with Federico Ardila axioms on diversity.

Axiom 1

Mathematical talent is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.

Axiom 2

Everyone can have joyful, meaningful, and empowering mathematical experiences.

Axiom 3

Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.

Axiom 4

Every student deserves to be treated with dignity and respect.