Matteo Fornoni, Ph.D.

Dipartimento di Matematica ''F. Casorati''
Università degli Studi di Pavia • Via Ferrata 5, 27100 Pavia, Italy
matteo.fornoni@unipv.it

ABOUT ME

I am currently a postdoctoral researcher in Mathematical Analysis at the University of Pavia, under the supervision of Prof. Elisabetta Rocca. My research focuses on the mathematical analysis of Partial Differential Equations, mostly of evolutionary type, and partly on Calculus of Variations. I am mainly concerned with studying analytical properties of mathematical models concerning biological phenomena such as tumour growth. In particular, I study systems of PDEs of Cahn-Hilliard or Allen-Cahn type and tackle problems regarding well-posedness, regularity, long-time behaviour, optimal control and inverse identification of initial data for these models.

EDUCATION

  • 2024-present: postdoctoral researcher in Mathematical Analysis at the University of Pavia.

  • 2021-2024: PhD in Mathematical Analysis under the joint PhD program between University of Pavia, University of Milano-Bicocca and INdAM.
    Thesis: Towards personalised tumour forecasting: mathematical analysis, optimal control and inverse identification,
    Supervisors: Prof. E. Rocca and Prof. C. Cavaterra.

    • Sept.-Dec. 2023: During my PhD, I had the pleasure of being a guest in the Applied Mathematics & Modelling group led by Prof. Ulisse Stefanelli at the University of Vienna.

  • 2018-2021: Master Degree in Mathematics University of Milan, 110/110 cum laude,
    Thesis: Mosco convergence of H^1 spaces and application to the stability of scattering problems,
    Supervisor: Prof. L. Rondi.

  • 2015-2018: Bachelor Degree in Mathematics, University of Milan, 110/110 cum laude.

PUBLICATIONS

  1. E. Beretta, C. Cavaterra, M. Fornoni, M. Grasselli, Optimal control of the fidelity coefficient in a Cahn-Hilliard image inpainting model, preprint arXiv:2502.03025 [math.OC] (2025).

  2. A. Agosti, E. Beretta, C. Cavaterra, M. Fornoni, E. Rocca, Identifying early tumour states in a Cahn-Hilliard-reaction-diffusion model, preprint arXiv:2409.15925 [math.AP] (2024).

  3. E. Beretta, C. Cavaterra, M. Fornoni, G. Lorenzo, E. Rocca, Iterative algorithms for the reconstruction of early states of prostate cancer growth, preprint arXiv:2409.12844 [math.AP] (2024).

  4. E. Beretta, C. Cavaterra, M. Fornoni, G. Lorenzo, E. Rocca, Mathematical analysis of a model-constrained inverse problem for the reconstruction of early states of prostate cancer growth, SIAM J. Appl. Math. 84 (2024), 2000-2027, https://doi.org/10.1137/24M1655469.

  5. M. Fornoni, Maximal regularity and optimal control for a non-local Cahn-Hilliard tumour growth model, J. Differential Equations 410 (2024), 382-448, https://doi.org/10.1016/j.jde.2024.07.036.

  6. M. Fornoni, Optimal distributed control for a viscous non-local tumour growth model, Appl. Math. Optim. 89, 8 (2024), https://doi.org/10.1007/s00245-023-10076-4.

  7. M. Fornoni, L. Rondi, Mosco convergence of Sobolev spaces and Sobolev inequalities for nonsmooth domains, Calc. Var. Partial Differential Equations 62, 15 (2023), https://doi.org/10.1007/s00526-022-02357-7.

UPCOMING EVENTS

  • April 6-18, 2025, Research visit at NYU Abu Dhabi, Abu Dhabi (UAE), by invitation of prof. E. Beretta.

  • May 11-25, 2025, Research visit at Fudan University, Shanghai (China), by invitation of prof. H. Wu.

TALKS AND CONFERENCES

  • Incontro Annuale dei Ricercatori in Matematica UNIPV, Università degli Studi di Pavia, Pavia, Italy, February 5-6, 2025, invited talk ''Phase-field tumour growth models: analysis, control and inverse reconstruction''.

  • The 14th AIMS Conference on Dynamical Systems and Differential Equations, Abu Dhabi (UAE), December 16-20, 2024, invited talks ''Reconstructing early stages of prostate cancer growth'' at SS19 and ``Maximal regularity and optimal control for a non-local Cahn Hilliard tumour growth model'' at SS24.

  • Italian-Japanese Workshop on Variational Perspectives for PDEs, Università degli Studi di Pavia, Pavia, Italy, September 9-13, 2024, invited talk ''Reconstructing early stages in a Cahn-Hilliard tumour growth model''.

  • CIME Course: Diffuse Interface methods in Continuum Mechanics: analysis, singular limits and algorithms, Cetraro, Italy, July 8-12, 2024, poster presentation ''Inverse reconstruction of early stages for a Cahn-Hilliard tumour growth model''.

  • Lions-Magenes days 2024, Università degli Studi di Pavia, Pavia, May 21-22, 2024, invited talk ''Reconstructing early stages of prostate cancer growth''.

  • Conference: The Cahn-Hilliard equation - recent advances and new challenges, Chęciny, Poland, April 21-26, 2024, contributed talk ''Maximal regularity and optimal control for a Cahn-Hilliard tumour growth model''.

  • SITE Research Center Talk Series, weekly seminars of the research group led by N. Masmoudi, NYU Abu Dhabi, April 2, 2024, invited talk ''Optimal control for non-local Cahn-Hilliard tumour growth models''.

  • Bio-PDE Days Vienna, TU Wien, Vienna, February 28 - March 1, 2024, contributed talk ''Inverse identification of initial data for a prostate cancer model''.

  • INdAM Workshop ''Cahn-Hilliard and Allen-Cahn equations in bio-medicine'', Politecnico di Milano, February 22, 2024, organiser.

  • 3rd Austrian Calculus of Variations Day, TU Wien, Vienna, November 23-24, 2023, contributed talk ''Optimal control for non-local tumour growth models''.

  • Calculus of Variations Seminar, weekly seminar of the Applied Mathematics and Modelling group, University of Vienna, November 7, 2023, invited talk ''Optimal control for non-local tumour growth models''.

  • XXII Congresso dell'Unione Matematica Italiana, Pisa, September 4-9, 2023, special session SS6, invited talk ''Optimal distributed control for a non-local diffuse interface tumour growth model''.

  • HCM Workshop ''Nonlinear PDEs: Recent Trends in the Analysis of Continuum Mechanics'', Hausdorff Center for Mathematics, Bonn, July 17-21, 2023, contributed talk ''Optimal distributed control for a non-local diffuse interface tumour growth model''.

  • 93rd Annual GAMM Meeting, TU Dresden, May 30 - June 2, 2023, contributed talk ''Optimal distributed control for a non-local diffuse interface tumour growth model''.

  • MOCETIBI ''Modelling Cell and Tissue Biomechanics'' Workshop, LJLL, Sorbonne University, Paris, October 11-13, 2022, contributed talk ''Optimal distributed control for a non-local diffuse interface tumour growth model''.

  • Mathematical Biology on the Mediterranean Conference, 3rd edition, FORTH, Heraklion, Crete, August 28 - September 6, 2022, contributed talk ''Optimal distributed control for a non-local diffuse interface tumour growth model''.

  • PHAME2022 ''PHAse field MEthods in applied sciences'', INdAM Workshop, Rome, May 23-27, 2022, local organiser.

TEACHING

  • A.Y. 2024-2025, Mathematical Analysis 1 (with prof. E. Rocca), University of Pavia, exercise lectures (10 hours), degree course in Civil Engineering.

  • A.Y. 2024-2025, Elements of Mathematics, University of Pavia, lecturer in charge (12 hours), degree course in Natural Sciences.

  • A.Y. 2023-2024, Mathematical Analysis 2 (with prof. S. Lisini and prof. G. Schimperna), University of Pavia, exercise lectures (20 hours), degree course in Mathematics.

  • A.Y. 2023-2024, Mathematics (with prof. L. Rondi and prof. G. Schimperna), University of Pavia, exercise lectures (8 hours), degree course in Biology.

  • A.Y. 2022-2023, Mathematical Analysis 2 (with prof. S. Lisini and prof. A. Segatti), University of Pavia, exercise lectures (12 hours), degree course in Industrial Engineering.

  • A.Y. 2022-2023, Advanced Mathematical Methods for Engineers (with prof. E. Rocca), University of Pavia, lecturer (5 hours), masters degree course in Electronic Engineering.

  • A.Y. 2022-2023, Mathematical Analysis 1 (with prof. E. Rocca), University of Pavia, teaching assistant, degree course in Civil Engineering.

  • A.Y. 2022-2023, Geometry and Linear Algebra (with prof. A. Ghigi), University of Pavia, teaching assistant, degree course in Civil Engineering.

  • A.Y. 2021-2022, Mathematical Analysis 2 (with prof. M. Veneroni), University of Pavia, exercise lectures (4 hours), degree course in Bioengineering.

  • A.Y. 2021-2022, Mathematical Analysis 1 (with prof. E. Rocca), University of Pavia, exercise lectures (10 hours), degree course in Civil Engineering.