COLOMBO GIOVANNI

CURRICULUM VITAE, GIOVANNI COLOMBO

Personal and academic

Giovanni Colombo, Dipartimento di Matematica “Tullio Levi-Civita", Università di Padova,
via Trieste 63, 35121 Padova (Italy)
e-mail: colombo@math.unipd.it
personal web page: http://www.math.unipd.it/~colombo
telephone: +39 049 8271445
Full professor, MAT-05, Department of Mathematics, University of Padua.

- March 1988: “Doctor Philosophiae", (SISSA); advisor: prof. A.Cellina.
- March 1988 - March 1990: post doctoral position, SISSA, Trieste.
- April 1990 - October 1992: research assistant position, SISSA, Trieste.
- November 1992 - December 2004: associate professor, University of L'Aquila and Padova (Italy).
- December 2004 - present time: full professor, mathematical analysis, Department of Mathematics, University of Padova.


Selected research projects and visits

- 1993: collaboration with V. Krivan (Czech Academy of Sciences): funded with 8,000 ECU by EU (ERB-CIPA-CT-93-1554); research program: analysis of deterministic uncertain systems.
- 1999-2000: Local coordinator of a national project on Ordinary differential equations (PI: A. Cellina)
- 2001: collaboration with M. Monteiro Marques (CMAF, Lisbon): funded by Istituto Nazionale di
Alta Matematica; research program: analysis of Moreau's sweeping process.
- 2004-2005: PI of a Padova University research project.
- 2004: invited visit to CMAF, Lisbon.
- 2009: collaboration with V. Goncharov (Univ. of Evora, Portugal), funded by INdAM.
- 2010-2013: member of the research project VARIANT, funded by the Portuguese Ministry of Edu-
cation
- 2010-2014: member of EU Marie Curie Project “SADCO".
- 2015-2017: PI of the Padova University research project “Control of dynamics with active con-
straints".
- 2018: collaboration with P. Bettiol (Brest) funded by Université de Bretagne Occidentale.
- 2023-2025: PI of the national project PRIN 2022 "Optimal control problems: analysis, approximation and applications"

Editorial Boards

- Set Valued and Variational Analysis (2014 - present)
- Discussiones Mathematicae Differential Inclusions (2000 - present)

Organization of international conferences

Control of state constrained dynamical systems, Padova, September 2024.
Control of state constrained dynamical systems, Valparaiso, September 2019.
Control of state constrained dynamical systems, Padova, September 2017.
Analysis and Geometry in Control Theory and its Applications, INdAM Workshop, Roma, June 2014.
Nonlinear differential equations and control, celebrating A. Cellina's 70th birthday, Milano, September
2011.
Variational and differential problems with constraints, Venezia, September 2006.


Educational and service activities.

2017: PhD course “An introduction to the mathematical control theory and to set-valued analysis".
1990, 1991, 2001: PhD courses (Introduction to differential inclusions; set-valued and nonsmooth
analysis).
1992 - present: courses on Mathematical Analysis for the Engineering School (various levels) and
Master courses for mathematics (Calculus of Variations, Advanced Analysis)
1999 - present: member of various Faculty boards for teaching and research organization.
Oct. 2021 - present: coordinator of the PhD School in Mathematics, University of Padova.

Supervisor of research Master thesis (1989, 1994, 2014, 2018, 2021).

Supervisor of the following PhD students and post doc:
• A. Marigonda, 2002 - 2006; currently tenured (associate professor) at Verona University.
• Khai T. Nguyen, 2008 - 2010; currently tenured at North Carolina State University.
• Luong V. Nguyen, 2011 - 2014; currently tenured at Hong Duc University, Viet Nam.
• Thuy T.T. Le, 2013 - 2016; currently Research Associate at NIH, Ann Arbor, USA.
• Michele Palladino (2015), partial supervision, in collaboration with R. Vinter (Imperial College)
[supervisor]; currently tenure track (RTDb) at GSSI, L'Aquila.
• Chems Eddine Arroud (2015 - 2016), in collaboration with. T. Haddad, University of Jijel,
Algeria, currently tenured ad the University of Jijel, Algeria.
• Nathalie Khalil (2015 - 2016), partial supervision in collaboration with F. Rampazzo (Padova)
and P. Bettiol (Brest) [supervisor], currently post doc at FEUP, Porto.
• Paolo Gidoni (June 2018 - May 2019), post doctoral position funded by the INdAM project
Math. Tech., currently at Czech Academy of Sciences, Prague.
• Denis Shishmintsev, (Oct. 2022-); MCSA UNIPhD
• Nikolay Pogodaev (post doc, 2025)


Selected invited talks

- Krasiczyn (Poland), 1988 “International conference on differential inclusions”
- Warsaw, 1989, “Mini-Semester on Differential Inclusions"
- Pamporovo (Bulgaria), 1990
- Warsaw, 1993, “Mini-Semester on Differential Inclusions",
- Fontevraud (France), 1994, Conference “Viability and Control"
- Second Symposium on Nonlinear Analysis, Torun, 1999.
- Nonsmooth analysis and Mathematical control Theory, Baton Rouge, 2003.
- SISSA, 1993 (seminar);
- Firenze, 1996 (seminar);
- SISSA, 1997 (seminar);
- Roma “Tor Vergata”, 1997 (seminar);
- Politecnico di Torino, 1998 (seminar);
- Schauder lecture, Torun (Poland), 2003;
- Technical University, Budapest, 2003 (seminar);
- Conference “Geometric Control Theory and Nonsmooth Analysis”, INDAM, Rome, 2006;
- Conference “Control Theory and nonsmooth analysis”, INDAM, Rome, June 2009.
- ICIAM, Dresden, May 2010.
- ENSTA, Paris, March 2011: Kick-off meeting of the Marie Curie project “SADCO".
- Conference IFIP, Berlin, September 2011.
- Oberwolfach, Conference “Variational Methods for Evolution”, December 2011.
- Brescia University, March 2012 (seminar).
- Conference at International school “G. Stampacchia", Erice, May 2012.
- Conference in memoriam Francesco De Blasi, Rome, October 2012.
- SIAM Conference “Applications of Dynamical Systems”, Snowbird (Utah), May 2015: invited
session.
- SIAM conference on Control, Paris, July 2015: invited session.
- Conference for the 60th birthday of A. Bressan, SISSA, June 2016.
- Conference for the 60th birthday of A. Arutyunov, Porto, April 2017.
- School “MURPHYS", Technical University of Turin, June 2017.
- Conference for the 60th birthday of P. Cannarsa, INdAM, Roma, July 2017.
- School “Nonlinear Analysis and Applications", Irkutsk, June 2018.
- Brest, Université Bretagne Occidentale, 2018 (seminar).
- Workshop in memoriam V. Goncharov, Evora, November 2018.
- Workshop “EPCO 2019 - Portuguese Meeting on Optimal Control", June 2019.
- Workshop and school: Control of state constrained dynamical systems, Valparaiso, September 2019.
- Conference “MURPHYS 2022", Opava, May 2022.
- Workshop "Optimal Control Theory" (Rouen), June 22-24, 2022.
- Conference "Nonsmooth Problems with Applications in Mechanics", June 17 - 22, 2023, Będlewo.
- Conference "Nonsmooth And Variational Analysis", Dijon, June 26-28, 2023.
- International Mathematical School "G. Stampacchia", Erice, September 2024.


Citations (MathSciNet): 1082; H-index: 18 (as on 15.5.2025).

Research topics.

- Set-valued analysis (continuous selections without convexity assumptions)
- Differential inclusions (existence of solutions without convexity assumptions)
- Optimal control (existence of minimizers)
- Nonsmooth analysis (regularity properties of some value functions of optimal control problems, and
of some non-Lipschitz functions)
- Viability theory and Moreau's sweeping process (existence of solutions of differential inclusions with
various types of state constraints)
- Analysis of uncertain systems (deterministic perturbation; probabilistic approach for deterministic
perturbations)
- The regularity of the minimum time function and its numerical approximation (applications of nonsmooth analysis and of geometric measure theory to regularity properties of some value functions).
- Qualitative analysis and optimal control of Moreau's sweeping process (in particular, various approaches for necessary conditions).
- Geometric control theory under state constraints (a new construction of “neighboring feasible trajectories”).
Total publications: (Scopus): 54; (MathSciNet): 66.

Selected publications (full list at the URL https://www.math.unipd.it/~colombo/curring.pdf)
22) G. Colombo, Boris Mordukhovich, Dao Nguyen, Trang Nguyen, Discrete approximations and
optimality conditions for controlled free-time sweeping processes, Appl Math. Optim. 89 (2024),
Paper No. 40, 55 pp.
21) G. Colombo, N. T. Khalil, F. Rampazzo, State constraints, higher order inward pointing conditions, and neighboring feasible trajectories, SIAM J. Control Optim. 60 (2022), 3326-3357.
20) Tan H.Cao, G. Colombo, B. S. Mordukhovich, D. Nguyen, Optimization of fully controlled sweeping processes, J. Diff. Eq. 295 (2021), 138-186.
19) G. Colombo, P. Gidoni, On the optimal control of rate-independent soft crawlers, J. Math. Pures Appl. 46 (2021), 127-157.
18) G. Colombo, B. S. Mordukhovich, Dao Nguyen, Optimization of a perturbed sweeping process by constrained discontinuous controls, SIAM J. Control 58 (2020), 2678-2709.
17) Ch. E. Arroud, G. Colombo, A Pontryagin maximum principle for the controlled sweeping process, Set-Val. Var. Anal. 26 (2018), 607-629.
16) G. Colombo, M. Palladino, The minimum time function for the controlled Moreau's sweeping
process, SIAM J. Control 54 (2016), 2036-2062.
15) G. Colombo, Thuy T.T. Le, Higher order discrete controllability and the approximation of the
minimum time function, Discr. Cont. Dyn. Systems Ser. A 35 (2015), 4293-4322.
14) G. Colombo, Khai T. Nguyen, Luong V. Nguyen, Non-Lipschitz points and the SBV regularity
of the minimum time function, Calc. Var. PDE's (2013), 51 (2014), 439-463.
13) G. Colombo, V. V. Goncharov, Brownian motion and exposed solutions of differential inclusions (Dedicated to A. Cellina for his 70th birthday), NoDEA 20 (2013), 323-343.
12) G. Colombo, L. Thibault, Prox-regular sets and applications, in Handbook of Nonconvex Analysis, D.Y. Gao, D. Motreanu eds., International Press (2010), ISBN: 978-1-57146-200-8.
11) G. Colombo, Khai T. Nguyen, On the structure of the minimum time function, SIAM J. Control
48 (2010), 4776-4814.
10) G. Colombo, Khai T. Nguyen, Quantitative isoperimetric inequalities for a class of nonconvex sets, Calc. Var. PDE's 37 (2010), 141-166.
9) G. Colombo, A. Marigonda, P. Wolenski, Some new regularity properties for the minimal time
function, Siam J. Control 44 (2006), 2285-2299.
8) G. Colombo, A. Marigonda, Differentiability properties for a class of non-Lipschitz functions, Calc. Var. PDE's 25 (2006), 1-31.
7) G. Colombo, M. D.P. Monteiro Marques, Sweeping by a continuous phi-convex set, J. Differ.
Equations 187 (2003), 46-72.
6) G. Colombo, P. Dai Pra, A class of piecewise deterministic Markov processes, Markov Processes and Related Fields 7 (2001), 251-287.
5) G. Colombo, V. Goncharov, The sweeping processes without convexity, Set-Valued Anal. 7 (1999), 357-374.
4) A. Cellina, G. Colombo, On a classical problem of the calculus of variations without convexity
assumptions, Ann. Inst. H. Poincaré, Analyse Nonlinéaire 7 (1990), 97-106.
3) A. Bressan, A. Cellina, G. Colombo, Upper semicontinuous differential inclusions without convexity, Proc. Am. Math Soc. 106 (1989), 771-775.
2) A. Bressan, G. Colombo, Generalized Baire category and differential inclusions in Banach spaces, J. Differ. Equat. 76 (1988), 135-158.
1) A. Bressan, G. Colombo, Extensions and selections of maps with decomposable values, Studia
Mathematica 90 (1988), 69-86.