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.
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
D. Liessi, Pseudospectral methods for the stability of periodic solutions of delay models, PhD thesis, University of Udine, Italy, 2018. thesis (PDF, latest update 28/10/2019)
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.
Congresso UMI 2023,
U. Pisa and Scuola Normale Superiore (I),
4–9 September 2023,
sezione “S10 -- Sistemi dinamici e metodi numerici per le equazioni differenziali”,
Approssimazione degli esponenti di Lyapunov per equazioni di rinnovo,
invited.
Mathematical Modelling in Engineering & Human Behaviour 2023,
Universitat Politécnica de València (E),
11–14 July 2023,
session “Mathematical models in population dynamics: applications, modelling and numerical methods”,
Numerical bifurcation analysis of delay equations: a user-friendly MatCont interface,
invited.
17th IFAC Workshop on Time Delay Systems,
Montréal (CA),
27–30 September 2022,
invited session “Software for time delay systems”,
Numerical bifurcation analysis of delay equations: a user-friendly MatCont interface,
invited.
16th IFAC Workshop on Time Delay Systems,
Guangzhou (CHN),
online,
29 September – 1 October 2021,
invited session “Computational tools and software, II”,
Stability of equilibria and periodic orbits of delay equations,
invited.
6th ECCOMAS Young Investigators Conference,
Universitat Politécnica de València (E),
online,
7–9 July 2021,
minisymposium “Recent advances in time numerical integration of evolutive problems”,
Numerical stability analysis of linear periodic delay equations via pseudospectral methods,
invited.
Online Delay Days,
Hasselt (B) – Utrecht (NL) – Berlin (D),
1–2 October 2020,
Numerical stability analysis of linear periodic renewal equations via pseudospectral methods,
invited.
Convegno GNCS 2020,
Montecatini Terme (I),
11–13 February 2020,
Approximation of the spectrum of evolution operators for linear neutral delay equations with pseudospectral methods,
invited.
14th IFAC Workshop on Time Delay Systems,
Budapest (H),
28–30 June 2018,
thematic session “Numerical analysis for delay equations in population dynamics”,
Pseudospectral methods for the stability of periodic solutions of delay equations.
14th IFAC Workshop on Time Delay Systems,
Budapest (H),
28–30 June 2018,
thematic session “Spectral methods for rightmost roots characterization in LTI time delay systems”,
Pseudospectral approximation of characteristic roots and multipliers: how multiplicities affect convergence.
CRM conference: New Trends in Mathematical Biology,
CRM – Centre de Recerca Matemàtica,
Barcelona (E),
4–8 June 2018,
Pseudospectral methods for the stability of periodic solutions of delay equations.
Biomathematics Seminars,
U. Helsinki (FI),
20 September 2018,
Stability of periodic solutions of delay equations: from Floquet theory to pseudospectral collocation,
invited.
DMIF, U. Udine (I),
28 July 2016,
Introduzione al calcolo dell’esponenziale di matrice.
DMIF, U. Udine (I),
22 Aprile 2016,
Analisi degli errori per il metodo di Galërkin.
DMIF, U. Udine (I),
7 January 2016,
Stability of periodic solutions of physiologically structured populations: a promising extension of the solution operator approach.
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.
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.
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.
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 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
Dobbiaco Summer School 2023,
Dobbiaco (I),
18–23 June 2023,
theme Data-driven methods for the computational sciences,
lecturers: Nathan Kutz, Karsten Urban.
Advanced School on Controlling delayed dynamics: advances in theory, methods and applications,
CISM – International Centre for Mechanical Sciences,
Udine (I),
25–29 November 2019,
lecturers: Dimitri Breda, Tamás Insperger, Bernd Krauskopf, Wim Michiels, Silviu-Iulian Niculescu, Sjoerd Verduyn Lunel.
Szeged School on Computational Tools for Delay Differential Equations,
U. Szeged (HU),
9–11 September 2016,
lecturers: Balázs Bánhelyi, Dimitri Breda, Tibor Csendes, Ferenc Hartung, János Karsai, Gábor Kiss, Tibor Krisztin, Mónika Polner, Jan Sieber, Gabriella Vas, Zsolt Vizi, Hans-Otto Walther, Jianghong Wu.
Dobbiaco Summer School 2015,
Dobbiaco (I),
21–26 June 2015,
theme Innovative concepts for complexity reduction in numerical PDEs: nonlinear approximation, sparsity, adaptivity, model reduction,
lecturers: Claudio Canuto, Wolfgang Dahmen.
This page was last modified on 2023-12-28.
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