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January 2025

New lecture series

I am very happy to announce the launch of QuanTO – Quantum Lectures in Torino. This joint initiative is the result of the scientific cooperation among researchers from the Departments of Physics and Mathematics of Politecnico di Torino (DISMA-DISAT) and Università di Torino.

The inaugural event of this series will take place on January 30th, 2025. We are pleased to host Professor Benjamin Schlein from the University of Zürich on this occasion, who will talk about the

Bogoliubov Theory for Dilute Bose Gases.

Schedule and further details can be found in the website of the series. No registration is required, participation of young students and researchers is especially welcome. Join us and spread the word!

January 2025

New preprint

The preprint Compressed sensing for inverse problems II: applications to deconvolution, source recovery, and MRI, a joint work with Giovanni S. Alberti, Alessandro Felisi and Matteo Santacesaria, is now available on arXiv (arXiv:2501.01929).

We expand the sample complexity theory for ill-posed inverse problems developed in a previous work, based on infinite-dimensional compressed sensing and generalized sampling techniques, in order to handle at once a variety of practical applications (including deconvolution, source recovery, wavelet-Fourier coefficient recovery).

December 2024

New website!

My old webpage (trapasso.altervista.org) has been discontinued.

Welcome to the new site (trapasso.info) – work in progress!

November 2024

Accepted paper

So proud to share that the article Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform, a joint work with Giovanni S. Alberti, Alessandro Felisi and Matteo Santacesaria, has been accepted for publication in Journal of the European Mathematical Society.

See arXiv:2302.03577 for the preprint and stay tuned for the upcoming chapters of the saga!

September 2024

Popularization at UNIGHT

UNIGHT (Notte Europea delle Ricercatrici e dei Ricercatori) is an annual research popularization event taking place in many European cities. We will celebrate this recurrence in Torino on September 27-28 with several activities.

I am involved in a joint sequence of scientific talks on topics at the edge between philosophy, physics and technology with a great team of colleagues from/visiting Politecnico di Torino (Riccardo Adami, Yuri Ardesi, Jordan François, Andrea Marchesin, Fabrizio Mo, Lucrezia Ravera, Vera Tripodi).

Come and join us on September 28 at Area Caffè C3 (Musei Reali – Giardini Reali, Piazzetta Reale 1) from 12.00 to 14.00!

August 2024

New preprint

The preprint Wave packet analysis of semigroups generated by quadratic differential operators is now available on arXiv (arXiv:2408.11130).

We perform a phase space analysis of evolution equations associated with the Weyl quantization \(q^{\text{w}}\) of a complex quadratic form \(q\) on \(\mathbb{R}^{2d}\) with non-positive real part. In particular, we obtain pointwise bounds (with sharp time dependence) for the matrix coefficients of the Gabor wave packet decomposition of the generated semigroup \(e^{tq^{\text{w}}}\), which are then leveraged to study boundedness on modulation spaces \(M^p(\mathbb{R}^d)\), \(1 \le p \le \infty\).

July 2024

New preprint

The preprint Phase space analysis of higher-order dispersive equations with point interactions, a joint work with Sonia Mazzucchi and Fabio Nicola, is now available on arXiv (arXiv:2407.15521).

We investigate nonlinear, higher-order dispersive equations with measure (or even less regular) potentials and initial data with low regularity. Our approach is of distributional nature and relies on the phase space analysis (via Gabor wave packets) of the corresponding fundamental solution – in fact, locating the modulation/amalgam space regularity of such generalized Fresnel-type oscillatory functions is a problem of independent interest in harmonic analysis.

April 2024

New preprint

The preprint Phase space analysis of finite and infinite dimensional Fresnel integrals, a joint work with Sonia Mazzucchi and Fabio Nicola, is now available on arXiv (arXiv:2403.20082).

The full characterization of the class of Fresnel integrable functions is an open problem in functional analysis, with significant applications to mathematical physics (Feynman path integrals) and the analysis of the Schrödinger equation. In finite dimension, we prove the Fresnel integrability of functions in the Sjöstrand class, broadly extending the current knowledge on the Fresnel integrability of Fourier transforms of finite complex measures, using techniques of Gabor wave packet analysis. We also discuss the problem of designing infinite dimensional extensions of this result in the general framework of projective systems of functionals.

April 2024

Workshop on quantum information

I am excited to announce that the workshop Mathematical Aspects of Quantum Information will take place at Politecnico di Torino on April 16-18, 2024.

This is the kick-off event of the GNAMPA INDAM Project 2024 Tecniche analitiche e probabilistiche in informazione quantistica. We are glad to host a minicourse by Nilanjana Datta (Cambridge) and lectures on diverse topics by experts like Marco Genovese (INRIM), Davide Girolami (Torino), Roberto Proietti (Torino) and Dario Trevisan (Pisa).

Further information and details on program and registration can be found in the website of the conference. Join us and spread the word!

April 2024

Visiting Aachen and Delft

I am grateful to the organizers of the workshop The ABCs of Sparsity and Singular Structures (RWTH Aachen, 3-5 April) for inviting me to give a short course on scattering transforms.

After the workshop I’ll be heading to Delft to visit Francesca Bartolucci and give a talk in the Analysis seminar at TU Delft.

January 2024

Conference talk @Ghent

I will join the conference Pseudo-Differential Operators and Related Topics organized by the Ghent Analysis & PDE Center. My talk will focus on the phase space analysis of the Hermite operator and related semigroups. Slides are available here.

December 2023

Conference talk @Aachen

I attended the workshop Analysis and its Applications at RWTH Aachen (18-19 Dec), where I had the privilege to join an amazing line-up of speakers. I gave a brief overview of the basics of wave packet analysis, along with some recent applications.

November 2023

Published papers

The article Stability of the scattering transform for deformations with minimal regularity, a joint work with Fabio Nicola, has been published (open access) in Journal de Mathématiques Pures et Appliquées. A copy of the manuscript is freely available here.

The article On heat equations associated with fractional harmonic oscillators, a joint work with Divyang Bhimani, Ramesh Manna, Fabio Nicola and Sundaram Thangavelu, has been published (open access) in Fractional Calculus and Applied Analysis. A copy of the manuscript is freely available here.

September 2023

Research in Pairs @CIRM

I will be in Trento from September 3 to 9 to continue the fruitful collaboration with Sonia Mazzucchi that began with our joint GNAMPA research project in 2022. On this occasion, my visit will be kindly supported by the Research in Pairs program of Centro Internazionale per la Ricerca Matematica (CIRM-FBK).

June 2023

Conference talk @Trondheim

I attended the delightful Workshop on Quantum Harmonic Analysis that took place at NTNU Trondheim (June 5-9), where I gave a talk on the existence of concentration optimizers in phase space — updated slides are available.

May 2023

Conference talk @Milano

I gave a talk at the XLII Convegno Nazionale di Analisi Armonica (Milano, May 29-31) concerning the existence of concentration optimizers in phase space — slides available here.

May 2023

Axioms 2022 Young Investigator Award

I am delighted to share that I have been awarded the Axioms 2022 Young Investigator Award. The prize is awarded to one under 35 nominated researcher “in recognition of their excellence in the field of mathematics, mathematical logic and mathematical physics”.

My deepest gratitude goes to the Award Committee and to all the mentors, friends and colleagues who have so far contributed to my training as a researcher.

November 2022

Published paper

The article On the existence of optimizers for time–frequency concentration problems, a joint work with Fabio Nicola and José Luis Romero, has been published in Calculus of Variations and Partial Differential Equations. A view-only copy of the paper is freely available via SharedIt here.

August 2022

Published book

The monograph Wave Packet Analysis of Feynman Path Integrals, written in collaboration with Fabio Nicola, has been published by Springer in the series Lecture Notes in Mathematics (vol. 2305).

Please visit the SpringerLink page of the book for more details and info on how to get a virtual or printed copy.

July 2022

Published paper

The paper On the Convergence of a Novel Time-Slicing Approximation Scheme for Feynman Path Integrals has been published in International Mathematics Research Notices. Pending assignment to an issue, the advance article is freely accessible here.

May 2022

Conference talk @Padova

The results of my Ph.D. thesis (selected among all the proposals by Ph.D. students in Italy over the years 2019-2022) have been presented at the international conference celebrating 100 years of Unione Matematica Italiana and 800 years of the University of Padova.