-> New preprint
Identifiability for mixtures of centered Gaussians and sums of powers of quadratics
joint work with A. Taveira Blomenhover (U. Kostanz), A. Casarotti (U. Trento), M. Michałek (U. Kostanz)
We consider the inverse problem for the polynomial map which sends an m-tuple of quadratic forms in n variables to the sum of their d-th powers. This map captures the moment problem for mixtures of m centered n-variate Gaussians. In particular, we study general identifiability.
-> The TensorDec Laboratory of U. of Trento is up and running!
Within the Department of Mathematics of the U. of Trento, we created the TensorDec Laboratory.
The lab wants to be a recipient for activities, both of research and formation. It aims to connect master and graduate students to the different aspects of the topic of tensor decompositions:
a 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.
Contact me if you want to know more or get involved in the activities of the lab.
-> I am a collaborator to the PopMat Laboratory of U. of Trento.
The lab is a joint project between the Department of Mathematics and the Department of Humanities and Philosophy and it is devoted to 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 popularisation, history and philosophy of mathematics jointly organised by the two departments since the last few years.
I agree with Federico Ardila axioms on diversity.
Mathematical talent is distributed equally among different groups,
irrespective of geographic, demographic, and economic boundaries.
Everyone can have joyful, meaningful,
and empowering mathematical experiences.
Mathematics is a powerful, malleable tool that can be shaped
and used differently by various communities to serve their needs.
Every student deserves to be treated with dignity and respect.
I obtained my Ph.D. in Mathematics in June 2016 at Stockholm University (Sweden) under the supervision of Boris Shapiro. From February to May 2015, I visited Enrico Carlini at Monash University (Australia).
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 (Spain). From April 2019 to March 2020, I was a Postdoctoral Fellow of the A. v. Humboldt Foundation (Germany) and I was part of the group of Thomas Kahle at OvGU Magdeburg.
Since April 2020, I am an Assistant Professor (Ricercatore RTD-b) at Università di Trento (Italy).
Here you can find my complete CV.
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 statistical models coming from phylogenetics or machine learning. These involve the study of Hilbert functions of 0-dimensional schemes and fat points, secant varieties of classical projective varieties as Veronese, Segre and Segre-Veronese varieties, apolarity theory and inverse systems.
Here is the full list of my research works.
Here is a selected list of slides from presentations.
Here are some of the problems that I like and I don't know how to solve.