* * * 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 work with Francesca Bartolucci and give a talk in the Analysis seminar at TU Delft.
* * * January 2024 – Conference talk * * *
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 * * *
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 paper * * *
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.
* * * November 2023 – Published paper * * *
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 * * *
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.
* * * June 2023 – New preprint * * *
The preprint Phase space analysis of spectral multipliers for the twisted Laplacian is now available on arXiv (arXiv:2306.00592).
We prove boundedness results on modulation and Wiener amalgam spaces concerning some spectral multipliers for the twisted Laplacian, including fractional heat and wave-type flows. Techniques of pseudo-differential calculus are inhibited due to the lack of global ellipticity of the special Hermite operator, therefore a phase space approach must rely on different pathways — e.g, transference principles leveraging on the metaplectic equivalence with a partial harmonic oscillator, or the twisted convolution structure of the eigenprojections.
* * * May 2023 – Conference talk * * *
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 – 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.
* * * February 2023 – New preprint * * *
The preprint 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 is now available on arXiv (arXiv:2302.03577).
We develop an infinite-dimensional compressed sensing framework that is powerful enough to cover a number of interesting settings at once, notably including some ill-posed inverse problems. In particular, rigorous estimates for the sample complexity of the sparse Radon transform (i.e., with a finite number of angles) are established for the first time.
* * * November 2022 – Conference talk * * *
Some recent results on the stability of scattering transforms (joint work with Fabio Nicola) were presented at the UMI workshop Matematica per l’Intelligenza Artificiale e il Machine Learning – Giovani ricercatori (Torino, Nov 24-26).
* * * 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.
* * * October 2022 – New preprint * * *
The preprint On heat equations associated with fractional harmonic oscillators, a joint work with Divyang Bhimani, Ramesh Manna, Fabio Nicola and Sundaram Thangavelu, is now available on arXiv (arXiv:2210.07691).
We establish some fixed-time decay estimates in Lebesgue spaces for the fractional heat propagator \(e^{-tH^{\beta}}\), \(t, \beta>0\), associated with the harmonic oscillator \(H=-\Delta + |x|^2\). We then prove some local and global wellposedness results for nonlinear fractional heat equations.
* * * September 20, 2022 – Minicourse * * *
I will give a short course on scattering networks at the Second Conference of Young Applied Mathematicians, which will take place in Arenzano (GE).
* * * 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.
* * * June 29, 2022 – Conference talk * * *
I have discussed some results on the wave packet analysis of Feynman path integrals at 11th International Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP2022), hosted online by the Stockholm University.
* * * June 13, 2022 – Conference talk * * *
Old and new results on mathematical path integrals have been presented at the Third Italian Meeting on Probability and Mathematical Statistics (Bologna).
* * * May 27, 2022 – Conference talk * * *
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.
* * * May 2022 – New preprint * * *
The preprint Stability of the scattering transform for deformations with minimal regularity, a joint work with Fabio Nicola, is now available on arXiv (arXiv:2205.11142).
In this note we elucidate the interplay between the scattering transform architecture and the regularity of the deformation in the \(C^\alpha\) regularity scale. We identify a structural stability threshold at \(\alpha=1\) (instability for \(0\le \alpha<1\), stability for \(\alpha >1\)). Stability is achievable even at the threshold, up to arbitrarily small losses.
* * * May 2022 – Funded research project * * *
I am happy to announce that the research project Analisi armonica e stocastica in problemi di quantizzazione e integrazione funzionale has been funded by GNAMPA (INdAM). I will coordinate the efforts of an exceptional, multidisciplinary team consisting of Francesco C. De Vecchi, Sonia Mazzucchi and Fabio Nicola.
* * * March – May 2022 – PhD course @UniGE * * *
Luca Ratti and I are glad to announce the forthcoming course Harmonic Analysis of Scattering Networks, which is part of the training offer of the Ph.D. Program in Mathematics and Applications at the University of Genova. We plan to offer live streaming of the lectures in order to promote participation of students and researchers from different institutions. More details on attendance and program on the course page here (mandatory registration before February 20).
* * * February 21, 2022 – Conference talk * * *
I will present a survey of recent advances in the wave packet analysis of Feynman path integrals at the International Conference Microlocal and Global Analysis, Interactions with Geometry, hosted online by the University of Potsdam.
* * * February 14, 2022 – Conference talk * * *
I will discuss some results on the convergence of a novel family of time slicing approximation operators for Feynman path integrals (based on a recent preprint of mine) at the International Conference One-Parameter Semigroups of Operators (OPSO) 2022, hosted online by HSE University (Nizhny Novgorod).
* * * December 20, 2021 – New preprint * * *
The preprint On the existence of optimizers for time-frequency concentration problems, a joint work with Fabio Nicola and José Luis Romero, is now available on arXiv (arXiv:2112.09675).
We consider the (open) problem of the maximum \(L^p\)-concentration in a subset of the time-frequency space for the ambiguity function of normalized signals in \(L^2(\mathbb{R}^d)\) and show that maximizing waveforms do exist. The proof is based on the concentration compactness principle, with time-frequency shifts as dislocations.
* * * November 4-5, 2021 – Poster presentation * * *
The poster Stability of DCNNs under deformations, based on my recent paper with F. Nicola, has been accepted at DEEPMATH 2021. The poster is available here.