14th IFAC Workshop on Time Delay Systems, Budapest (H), 30/06/2018

I am a postdoctoral researcher in Numerical analysis at the Department of Mathematics, Computer Science and Physics (DMIF) of the University of Udine (Italy), where I am also a member of the Computational Dynamics Laboratory (CDLab).

Contact information

davide.liessi@uniud.it
+39 0432 558224

Room SN16

Department of Mathematics, Computer Science and Physics (DMIF)
University of Udine
Via delle Scienze 206
33100 Udine UD
Italy
(map)

I am often in the CDLab (+39 0432 558410).

Office hours: up-to-date information is available at the university’s directory.
Consultation is always possible by appointment, either in presence or via Microsoft Teams.

UniUD directory, ORCID, Google Scholar, ResearchGate, GitHub, GitLab

Full scientific CV (PDF, latest update 28/12/2023)

Research interests

My research mainly concerns delay equations and the infinite-dimensional dynamical systems they generate.

I have been working on the stability of their periodic solutions in its analytic (principle of linearised stability and Floquet theory for renewal equations) and numerical aspects (pseudospectral collocation of the evolution operators of renewal equations, also coupled with delay differential equations).

I am interested in the study of stability for neutral delay equations, in the generalisation of pseudospectral methods in several directions (arbitrary families of nodes, Lyapunov exponents, partial differential equations), in the study of analytic and numerical linearisation techniques, in the applications to population dynamics and epidemiology.

Research

Positions

  • November 2023 – November 2024 (current): Postdoctoral researcher, sector MAT/08, DMIF, U. Udine (I).
  • May 2020 – May 2023: Research fellow (RTDA), sector MAT/08, DMIF, U. Udine (I).
  • April 2018 – March 2019: Postdoctoral researcher, sector MAT/08, DMIF, U. Udine (I).
  • December 2017 – current: Member of CDLab – Computational Dynamics Laboratory, DMIF, U. Udine (I).

Visits

  • 28 June – 1 July 2023: Visit to Francesca Scarabel (U. Leeds, UK), collaboration with Hil Meijer (U. Twente, NL), topics: extension of MatCont for delay equations.
  • 10–20 February 2019: Stay at U. Utrecht (NL), collaboration with Odo Diekmann and Sjoerd M. Verduyn Lunel, topics: perturbation theory and stability of neutral delay equations.
  • 27 February – 26 May 2017: Stay at U. Utrecht (NL), collaboration with Odo Diekmann and Sjoerd M. Verduyn Lunel, topics: sun-star calculus and Floquet theory for retarded functional differential equations and renewal equations, perturbation theory for neutral delay equations, delayed models for population dynamics.
  • 16–19 May 2016: Visit to Odo Diekmann (U. Utrecht, NL), collaboration with Dimitri Breda (U. Udine, I), Mats Gyllenberg (U. Helsinki, FI), H. Metz (U. Leiden, NL), F. Scarabel (U. Helsinki, FI) and R. Vermiglio (U. Udine, I), topics: retarded functional differential equations and renewal equations, delayed models for population dynamics.

Projects

  • MONDI – Modellistica numerica e data-driven per l’innovazione sostenibile (U. Udine, MUR DM 737, NextGeneration EU, CUP G25F21003390007), principal investigator Dimitri Breda (U. Udine, I), member.
  • Modelización y análisis numérico en problemas de evolución con aplicaciones a biología, economía y mecánica de fluídos (PID2020-113554GB-I00/AEI/10.13039/501100011033), Ministerio de Ciencia e Innovación (E) and European FEDER funds, member.
  • PRIN 2020: Integrated mathematical approaches to socio-epidemiological dynamics (n. 2020JLWP23, CUP E15F21005420006), principal investigator Andrea Tosin (U. Torino, I), member.
  • Finanziamento GNCS Giovani Ricercatori 2020–2021: Approssimazione dello spettro di operatori di evoluzione per equazioni di rinnovo neutrali lineari tramite metodi pseudospettrali, grant recipient.
  • GNCS 2020: Analisi numerica di sistemi evolutivi complessi, coord. Dimitri Breda (U. Udine, I), member.
  • Finanziamento GNCS Giovani Ricercatori 2018–2019: Approssimazione degli autovalori di operatori di evoluzione per equazioni differenziali con ritardo neutrali lineari tramite metodi pseudospettrali, grant recipient.
  • GNCS 2018: Approssimazione numerica di problemi di evoluzione: aspetti deterministici e stocastici, coord. Raffaele D’Ambrosio (U. L’Aquila, I), member.
  • PRID 2017: Sistemi dinamici e applicazioni, DMIF, U. Udine (I), coord. Fabio Zanolin (U. Udine, I), member.
  • GNCS 2017: Analisi e sviluppo di metodologie numeriche per certi tipi non classici di sistemi dinamici, coord. Stefano Maset (U. Trieste, I), member.
  • SPA-DISCO 2016: Systèmes à paramètres distribués avec contraintes, CNRS International Research Network, coord. Giorgio Valmorbida (L2S, CentraleSupélec, F), duration 5 years, member.
  • GNCS 2016: Analisi numerica di certi tipi non classici di equazioni di evoluzione, coord. Stefano Maset (U. Trieste, I), member.
  • GNCS 2015: Analisi numerica di sistemi dinamici infinito-dimensionali e non regolari, coord. Nicola Guglielmi (U. L’Aquila, I), member.

Review activity

  • Bulletin of Mathematical Biology
  • International Journal of Computer Mathematics
  • Mathematical and Computational Applications
  • Mathematical Biosciences and Engineering
  • Mathematics and Computers in Simulation
  • Numerical Algorithms
  • PLOS ONE
  • Rendiconti dell'Istituto di Matematica dell'Università di Trieste

Publications & software

Journal articles

  • [10] D. Breda and D. Liessi, A practical approach to computing Lyapunov exponents of renewal and delay equations, submitted, arXiv: 2310.15400 [math.NA, math.DS].
  • [9] D. Breda, D. Liessi, and S. M. Verduyn Lunel, Spectra of evolution operators of a class of neutral renewal equations: theoretical and numerical aspects, Appl. Numer. Math. (2023), DOI: 10.1016/j.apnum.2023.06.018, pre-published, arXiv: 2302.01160 [math.NA, math.DS], 2023.
  • [8] A. Andò, S. De Reggi, D. Liessi, and F. Scarabel, A pseudospectral method for investigating the stability of linear population models with two physiological structures, Math. Biosci. Eng., 20 (2023), pp. 4493–4515, DOI: 10.3934/mbe.2023208.
  • [7] F. Blanchini, D. Breda, G. Giordano, and D. Liessi, Michaelis–Menten networks are structurally stable, Automatica, 147, 110683 (2023), DOI: 10.1016/j.automatica.2022.110683.
  • [6] D. Breda, D. Liessi, and R. Vermiglio, Piecewise discretization of monodromy operators of delay equations on adapted meshes, J. Comput. Dyn., 9 (2022), pp. 103–121, DOI: 10.3934/jcd.2022004.
  • [5] D. Breda and D. Liessi, Floquet theory and stability of periodic solutions of renewal equations, J. Dynam. Differential Equations, 33 (2021), pp. 677–714, DOI: 10.1007/s10884-020-09826-7.
  • [4] D. Breda and D. Liessi, Approximation of eigenvalues of evolution operators for linear coupled renewal and retarded functional differential equations, Ric. Mat., 69 (2020), pp. 457–481, DOI: 10.1007/s11587-020-00513-9.
  • [3] D. Breda and D. Liessi, Approximation of eigenvalues of evolution operators for linear renewal equations, SIAM J. Numer. Anal., 56 (2018), pp. 1456–1481, DOI: 10.1137/17M1140534.
  • [2] V. Clamer, A. Pugliese, D. Liessi, and D. Breda, Host coexistence in a model for two host–one parasitoid interactions, J. Math. Biol., 75 (2017), pp. 419–441, DOI: 10.1007/s00285-016-1088-z.
  • [1] D. Breda, O. Diekmann, D. Liessi, and F. Scarabel, Numerical bifurcation analysis of a class of nonlinear renewal equations, Electron. J. Qual. Theory Differ. Equ., 65 (2016), pp. 1–24, DOI: 10.14232/ejqtde.2016.1.65.

Book chapters

  • D. Breda, D. Liessi, and R. Vermiglio, A practical guide to piecewise pseudospectral collocation for Floquet multipliers of delay equations in MATLAB, submitted, arXiv: 2203.12734 [math.NA].
  • A. Andò, D. Breda, D. Liessi, S. Maset, F. Scarabel, and R. Vermiglio, 15 years or so of pseudospectral collocation methods for stability and bifurcation of delay equations, in G. Valmorbida, W. Michiels, and P. Pepe, eds., Accounting for Constraints in Delay Systems, Adv. Delays Dyn., Springer, Cham, 2022, pp. 127–149, DOI: 10.1007/978-3-030-89014-8_7.

Theses

Software

The listed software is available at CDLab.

  • D. Liessi, LE-RE, MATLAB codes for approximating Lyapunov exponents for renewal, also coupled with delay differential equations.
  • D. Liessi, eigTMNpw, MATLAB/Octave program extending eigTMNc (see below) in a piecewise fashion.
  • D. Breda and D. Liessi, eigTMNc, MATLAB/Octave program for approximating the spectrum of evolution operators of coupled systems of renewal equations and retarded functional differential equations.

Conferences, seminars & posters

Organisation of conference sessions

Conference talks

Seminars

Posters

Teaching

  • Support and exercise lessons of Calculus, BSc in Internet of Things, Big Data, Machine Learning, U. Udine (I), 60–120 hours, March–June 2024.
  • Laboratory sessions in the Advanced Course on Delays and structures in dynamical systems: Modeling, analysis and numerical methods in collaboration with Alessia Andò and Tedi Ramaj, CISM – International Centre for Mechanical Sciences, Udine (I), 5 hours, 20–24 November 2023; coordinators}: Dimitri Breda, Jianhong Wu; other lecturers: Odo Diekmann, Tony Humphries, Stefano Maset, Shigui Ruan, Francesca Scarabel, Rossana Vermiglio.
  • Mathematics, BSc in Banking and Finance, U. Udine (I), 72 hours, September–December 2023.
  • Laboratory of computational mathematics, MSc in Mathematics, U. Udine (I), 24 hours, February–April 2023.
  • Exercise lessons of Calculus, BSc in Computer Science and in Internet of Things, Big Data, Machine Learning, U. Udine (I), 24 hours, October 2022 – April 2023.
  • Mathematics, BSc in Banking and Finance, U. Udine (I), 72 hours, October–December 2022.
  • Laboratory of computational mathematics, MSc in Mathematics, U. Udine (I), 24 hours, March–June 2022.
  • Exercise lessons of Scientific computing, BSc in Computer science, U. Udine (I), 8 hours, March–June 2022.
  • Exercise lessons of Calculus, BSc in Computer Science and in Internet of Things, Big Data, Machine Learning, U. Udine (I), 24 hours, September 2021 – June 2022.
  • Exercise lessons of Mathematics, BSc in Banking and Finance, U. Udine (I), 10 hours, March–April 2022.
  • Mathematics, BSc in Banking and Finance, U. Udine (I), 72 hours, September–December 2021.
  • Laboratory of computational mathematics, MSc in Mathematics, U. Udine (I), 24 hours, March–June 2021.
  • Exercise lessons of Scientific computing, BSc in Computer science, U. Udine (I), 8 hours, March–June 2021.
  • Algebra I, BSc in Mathematics, U. Udine (I), 20 hours, September 2020 – June 2021.
  • An introduction to the numerical study of dynamical systems, U. Valladolid (E), 8+2 hours, April 2021, funded by the Erasmus+/KA1 Staff Mobility for Teaching Assignment program. course materials
  • Introductory course of basic mathematics, BSc in Computer Science and in Internet of Things, Big Data, Machine Learning, U. Udine (I), 20 hours, September 2020.
  • Exercise lessons of Numerical methods for differential equations, MSc in Mathematics, U. Udine (I), 6 hours, May–June 2020.
  • Laboratory of computational mathematics, MSc in Mathematics, U. Udine (I), 8 hours, May 2020.
  • Exercise lessons of Mathematics, BSc in Banking and Finance, U. Udine (I), 30+10 hours, October–December 2019.
  • Introductory course of Mathematics, BSc in Banking and Finance, U. Udine (I), 24 hours, August–September 2019.
  • Introduction to MATLAB, BSc and MSc in Engineering, U. Udine (I), 20 hours, March–May 2019.
  • Exercise lessons of Mathematics and statistics, BSc in Multimedia science and technology, U. Udine (I), 24 hours, October 2018 – June 2019.
  • Substitute teacher of Mathematics and physics, I.S.I.S.S. “F. Da Collo” (high school), Conegliano (I), November–December 2017.
  • Exercise lessons of Scientific computing, BSc in Computer science, U. Udine (I), 8 hours, October–December 2016.
  • Exercise lessons of Scientific computing, BSc in Computer science, U. Udine (I), 8 hours, October–December 2015.
  • Introduction to MATLAB for Numerical analysis II, MSc in Mathematics, U. Udine (I), 4 hours, October 2015.

Theses supervision

  • Enrico Santi, Numerical bifurcation analysis of delay equations: a user-friendly extension of MatCont's interface, BSc in Computer science, 2022, U. Udine (I), co-advisor (advisor Rossana Vermiglio).

Education

Degrees

  • 2014–2018: PhD in Computer Science, Mathematics and Physics, U. Udine (I), cum laude, thesis Pseudospectral methods for the stability of periodic solutions of delay models (PDF, latest update 28/10/2019), supervisor Dimitri Breda.
  • 2011–2014: MSc in Mathematics, U. Udine (I), cum laude, thesis Un modello per la dinamica dell’impatto tra martelletto e corda nel pianoforte, advisor Fabio Zanolin, co-advisors Dimitri Breda, Federico Fontana.
  • 2007–2011: BSc in Mathematics, U. Udine (I), cum laude, thesis Il gruppo degli automorfismi di un gruppo abeliano, advisor Dikran Dikranjan.

Participation in schools