Curriculum Vitæ of Lorenzo Luperi Baglini
University of Milan
Department of Mathematics
Via Cesare Saldini, 50
Milano 20133, Italy
September 2022
e-mail: lorenzo.luperi@unimi.it
website: https://sites.unimi.it/Luperi_Baglini/

Qualifications

2018 Italian Habilitation for Associate Professor in Mathematical Logic, ssd 01/A1.
2012 Ph.D. in Mathematical Logic and Computer Science, University of Siena, with a thesis in nonstandard analysis and combinatorial number theory entitled Hyperintegers and nonstandard techniques in combinatorics of numbers.
Advisors: Professor Mauro Di Nasso and Professor Franco Montagna.
Final Grade: Excellent.
01/2010 - 04/2010 Visiting Student in the program “Mathematical logic and foundations”, Equipe de Logique, University Paris 7.
2008 Master Degree in Mathematics, University of Pisa, with a thesis in nonstandard analysis entitled "Un nuovo modo di contare l’infinito" (A new way of counting the infinite).
Advisor: Professor Mauro Di Nasso.
Final grade: 110/110 with merit.
2006 Bachelor Degree in Mathematics, University of Pisa, with a thesis in model theory entitled "Una
classe di modelli della teoria dei campi reali chiusi con esponenziazione"
(A class of models of real closed field theory with exponentiation).
Advisor: Professor Mauro Di Nasso.
Final Grade: 110/110 with merit.
Academic Employment
06/2022 Associated Professor (PA) in Mathematical Logic, ssd 01/A1, Department of Mathematics “Federigo Enriques”, University of Milan.
06/2019 Researcher position (RTD B) in Mathematical Logic, ssd 01/A1, Department of Mathematics “Federigo Enriques”, University of Milan.
11/2017 -04/2022 Senior PostDoc position in the FWF Stand-Alone project “Nonstandard methods for Ramsey theory”, supported by grant P 30821-N35 of the Austrian Science Fund FWF, University of Vienna. The main topic of the project is the development of methods of nonstandard analysis to study several arguments in Ramsey theory, in particular the partition regularity of nonlinear Diophantine and exponential equations.
06/2017 - 10/2017 Senior PostDoc position in the FWF Stand-Alone project “Colombeau Algebras: Structure Theory and Regularity”, supported by grant P26859-N25 of the Austrian Science
Fund FWF, Wolfgang Pauli Institute, Vienna. The main topic of the project was the development of functional analysis methods for Colombeau algebras and their applications. The project leader of this Stand-Alone project was PhD Eduard Nigsch.
06/2015 - 05/2017 Senior PostDoc position in the FWF Lise-Meitner project “Applied Nonstandard Analysis”, supported by grant M1876-N35 of the Austrian Science Fund FWF, University of Vienna. The main topics of the project were applications of nonstandard analysis to PDE, functional analysis, combinatorial number theory and differential geometry, as well as applications of Colombeau’s generalized functions and generalized smooth functions to ODE. I was the project leader of this Lise-Meitner project, and the coapplicant of the project was Professor Michael Kunzinger (University of Vienna).
06/2013 - 05/2015 Senior Postdoc position in the project “Non-Archimedean Geometry and Analysis”,
supported by grant P25311-N25 of the Austrian Science Fund FWF, University of Vienna. The main topics of the project were non-Archimedean fields, Colombeau algebras, ultrafunctions and nonstandard analysis. The project leader was PhD Paolo Giordano, and the co-authors of the project were Professor Michael Kunzinger (University of Vienna) and Professor Vieri Benci (University of Pisa).
06/2012 - 05/2013 Holder of a research grant for the research project “Nonstandard methods in the study
of nonlinear phenomena”, University of Pisa. The project leader was Professor Vieri
Benci. The project was mainly devoted to develop the notion of ultrafunction and its
applications to some problems in mathematical analysis.

Research Interests
• Mathematical Logic and its applications.
• Combinatorial number theory by means of nonstandard analysis and ultrafilters methods.
• Applications of nonstandard analysis to analysis and mathematical physics.
• Non-Archimedean analysis.

Personal Research Grants
Since 2012, I have been awarded a total of EUR 526063.40, divided as follows:
• FWF Stand-Alone Position P 30821-N35, Nonstandard methods for Ramsey theory, University of Vienna, duration: 11/2017-10/2020, granted sum: EUR 343497.12.
• FWF Lise-Meitner Position M 1876-N35, Applied Nonstandard Analysis, University of Vienna,
duration: 06/2015-05/2017, granted sum: EUR 159620.00.
• Research project Nonstandard methods in the study of nonlinear phenomena, University of Pisa,
duration: 06/2012-05/2013, granted sum: EUR 22946.28.

Other Research Grants
I have been a co-applicant (with different roles) in the following funded research projects:
• SEED Research Grant for the project Sentinel: Situational awareness in critical Infrastructure Environment, University of Milan, duration: 05/2020-11/2021, granted sum: EUR 30000.00. Project
role: head of Department unit.

Teaching Experience
2020 - ongoing Teacher, “Logica Matematica 1” for Mathematics, University of Milan.
2019 - ongoing Teacher, “Matematica del Discreto” for SSRI and SSRI Online, Informatics, University
of Milan.
2019 - Assistant Teacher, “Matematica del Continuo” for SSRI and SSRI Online, Informatics,
University of Milan.
05/2019 - Invited teacher, short course “Nonstandard combinatorics”, Mathematics Department,
University of Warwick.
03/2016 - 06/2016 Teacher, “Nonstandard Analysis and Applications” for the Master Studies in Mathematics, class of Analysis, University of Vienna.
09/2011 - 05/2013 Assistant Teacher, “Analisi Matematica 2 e Complementi di Analisi Matematica” for
Chemical Engineering, Electrical Engineering and Energy Engineering, University of Pisa.

Research Stays
05/2019 Mathematics Department, University of Warwick, invited by L. Hong, 14-17 May.
03/2017 Mathematics Department, University of Kaiserslautern, invited by S. Trenn, 20-23
March.

Supervision of students and Postdocs
2022 Master Thesis, Michele Poli, “Metodi nonstandard per l’analisi matematica” (provisional title), to be defended, Department of Mathematics, University of Milan.
2021 Master Thesis, Matteo Barison, “Una numerosità aristotelica”, Department of Mathematics, University of Milan.
2020 - ongoing: Paulo Henrique De Souza Macedo Arruda, PhD Student, Department of Mathematics,
University of Vienna.
2018 Kyrylo Simonov, Postdoc position in the project “Nonstandard Methods in Ramsey Theory”, Department of Mathematics, University of Vienna.
2016 Bachelor Thesis, Helmut Geyer, “A nonstandard proof of Ramsey Theorem”, Department of Mathematics, University of Vienna.

Awards
2009 Winner of the “Premio AILA 3+2 2009” prize awarded to best bachelor and best master degree theses in mathematical logic with the thesis “Un nuovo modo di contare l’infinito”.
2007 Winner of the “Premio AILA 3+2 2007” prize awarded to best bachelor and best master degree theses in mathematical logic with the thesis “Una classe di modelli della teoria dei campi reali chiusi con esponenziazione”.

Invitations
2022 Invited teacher of the course “Teoria dei modelli e analisi non standard”, AILA summer school in Logic, Gargnano, Italia, 22-27 August 2022.
2022 Invited seminar for the Logic Seminar Semester in Caserta, Italia, 6 May 2022.
2022 Invited speaker to “International Conference on Mathematical Analysis and Applications, 2022 (ICOMAA-2022)”, Kalyani University, West Bengali, India, held online, 27-28 June 2022.
2021 Invited speaker to “Futuristic Trends in Mathematics 2021”, Midnapore City College, West Bengali, India, held online, 7-8 September 2021.
2021 Invited speaker to the “X Giornata di Analisi Nonstandard”, University of Verona, Italy, held online, 13 March 2021.
2019 Invited speaker to the workshop “Advances and Challenges in Nonlinear Analysis . . .and Beyond!”, University of Bari and Polytechnic of Bari , Bari, Italy, 24-27 September 2019.
2019 Invited speaker at the University of Warwick, Warwick, UK, 14-17 May. Title of the talk: Partition regularity of nonlinear Diophantine equations.
2019 Invited speaker to the special session “Applications of Ultrafilters and Nonstandard Methods”, AMS Sectional Meeting, University of Hawaii, Honolulu, Hawaii, 22-24 March 2019.
2018 Invitation at the “UMI-Simai-PTM Joint Meeting Wroc law”, University of Wroclaw, Wroclaw, Poland, 17-20 September. Title of the talk: Nonstandard methods in combinatorics.
2018 Invited speaker at the workshop “Ramsey Theory in Logic, Combinatorics and Complexity, RaTLoCC18”, Bertinoro International Center for Informatics, Italy, 15-20 July.
Title of the talk: Partition regularity of nonlinear Diophantine equations.
2018 Invitation at the 16th annual workshop on Combinatorial and Additive Number Theory
(CANT 2018), CUNY Graduate Center, New York, 22-25 May (invitation declined due to personal reasons).
2018 Invitation at the conference IIIM2018 (Incontro Italiano Insiemi e Modelli), University
of Turin, Turin, 21-23 February. Title of the talk: Nonstandard characterizations of partition regularity.
2017 Invited speaker at the workshop “Nonlinear Days in Turin”, University of Turin, Turin,
Italy, 21-22 September. Title of the talk: Fixed point methods for singular nonlinear differential equations.
2017 Invited speaker at the 10th Workshop on Nonlinear Differential Equations, University
of Brasilia, Brasilia, Brazil, 04-08 September (invitation declined due to personal reasons).
2017 Invitation at the workshop “Nonstandard methods in combinatorial number theory”,
American Institute of Mathematics, San José, California, 14-18 August.
2017 Invited speaker at the University of Kaiserslautern, Kaiserslautern, Germany, 20-23 March. Title of the talk: Non-Archimedean analysis and generalized functions.
2016 Invited speaker at the international workshop ”Achievements and Perspectives in Nonlinear
Analysis. A tribute to Donato Fortunato”, University of Bari, 14-17 June.

Organization of conferences and courses
2022 Organizer of the international conference “UltraMath 2022”, University of Pisa, Pisa, 6-11 June.
2018 Organizer of the workshop “Ramsey Theory of Equations and related topics”, University of Pisa, Pisa, 16-17 February.

Other Conferences and Presentations
2018 Participation at the workshop “Arithmetic Ramsey Theory in Manchester”, University of Manchester, Manchester, 10-13 September.
2017 Participation at the workshop “Ultrafilters, Ramsey theory and dynamics”, University of Lyon, Lyon, 20-24 November.
2017 Speaker at the “XXVI Incontro AILA” organized by AILA, University of Padova, Padova, 25-28 September. Title of the talk: Non standard methods in combinatorial number theory.
2017 Participation at the workshop “Nonstandard methods in combinatorial number theory”, American Institute of Mathematics, San Jos´e, California, 14-18 August.
2016 Speaker at the “International conference on generalized functions”, Dubrovnik, Croazia, 4-9 September. Title of the talk: Solving ODEs in GSF spaces: fixed point methods and distributions.
2016 Speaker at the workshop and conference “WING 2016, Workshop and Conference:
Wien-Innsbruck-Novi Sad-Gent”, University of Innsbruck, 29 June - 3 July. Title of the talk: Picard-Lindel¨of Theorems for GSF.
2016 Speaker at the international workshop ”Achievements and Perspectives in Nonlinear Analysis. A tribute to Donato Fortunato”, University of Bari, 14-17 June. Title of the talk: New spaces of generalized functions.
2015 Speaker at the conference “10th International ISAAC Congress”, University of Macau, 3-8 August. Title of the talk: A fixed point method for arbitrary generalized ODE.
2014 Speaker at the conference “International Conference on Generalized Functions GF2014”, University of Southampton, 7-13 September. Title of the talk: Asymptotic Gauges and the category of Colombeau algebras.
2014 Speaker at the conference “XXV Incontro AILA” organized by AILA, Scuola Normale Superiore, Pisa, 14-17 April. Title of the talk: Nonstandard techniques in combinatorial number theory.
2013 Speaker at the conference “EUROCOMB 2013”, Area della ricerca del CNR, Pisa,
9-13 September. Title of the talk: Partition regularity of nonlinear polynomials: a nonstandard approach.
2013 Speaker at the conference “Logic Colloquium 2013”, ´Evora, 22-27 July. Title of the
talk: Ultrafunctions: basic properties and a model problem.
2013 Speaker at the workshop “ULTRA-COMBINATORICS. Applications of ultrafilters in combinatorial number theory, and related topics”, Centro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore, Pisa, 24-25 January. Title of the talk: Partition Regularity of Nonlinear Polynomials.


Published papers
Scientific Journals
1. V. Benci, L. Luperi Baglini, Euclidean numbers and numerosities, J. Symbolic Logic, 1-40 (2022), https://doi.org/ 10.1017/jsl.2022.17.
2. L. Luperi Baglini, P.H. Arruda, Rado equations solved by linear combinations of idempotent ultrafilters, Topology Appl. 305 (2022), https://doi.org/10.1016/j.topol.2021.107897.
3. L. Luperi Baglini, Partition regularity of polynomial systems near 0, Semigr. Forum 103 (2021), 191–208, https://doi.org/10.1007/s00233-021-10179-w.
4. R. Scandone, L. Luperi Baglini, K. Simonov, A characterization of singular Schrodinger operators on the half-line, Canad. Math. Bull. (2020), 1-19. doi:10.4153/S0008439520000958.
5. L. Luperi Baglini, Nonstandard characterisations of tensor products and monads in the theory of ultrafilters,
Math. Log. Quart. 65 (2019), 347–369 (2019), DOI 10.1002/malq.201800089.
6. V. Benci, L. Luperi Baglini, K. Simonov, Infinitesimal and infinite numbers as an approach to quantum mechanics, Quantum 3, 137 (2019), Doi: https://doi.org/10.22331/q-2019-05-03-137.
7. V. Benci, L. Luperi Baglini, M. Squassina, Generalized solutions of variational problems and applications, Adv. Nonlinear Anal. (2018), https://doi.org/10.1515/anona-2018-0146.
8. M. Di Nasso, L. Luperi Baglini, Ramsey properties of nonlinear Diophantine equations, Adv. Math., Vol. 324 (2018), 84–117, DOI: https://doi.org/10.1016/j.aim.2017.11.003.
9. A. Lecke, L. Luperi Baglini, P. Giordano, The classical theory of calculus of variations for generalized smooth functions, Adv. Nonlinear Anal. (2017), https://doi.org/10.1515/anona-2017-0150
10. V. Benci, L. Luperi Baglini, Generalized solutions in PDE’s and the Burgers’ equation, J. Diff. Eq., Vol. 263 (2017), Issue 10, 6916–6952, DOI: https://doi.org/10.1016/j.jde.2017.07.034.
11. L. Luperi Baglini, P. Giordano, The category of Colombeau algebras, Monatsh. Math., Vol. 182 (2017), Issue 3, 649–674, doi: 10.1007/s00605-016-0990-1.
12. L. Luperi Baglini, F-finite embeddabilities of sets and ultrafilters, Arch. Math. Logic, Vol. 55 (2016), Issue 5, 705–734, doi: 10.1007/s00153-016-0489-4.
13. P. Giordano, L. Luperi Baglini, Asymptotic gauges: generalization of Colombeau type algebras, Math. Nachr., Vol. 289 (2016), Issue 2-3, 247–274, doi: 10.1002/mana.201400278.
14. V. Benci, L. Luperi Baglini, A non-archimedean algebra and the Schwartz impossibility theorem, Monatsh. Math., Vol. 176 (2015), 503–520, doi: 10.1007/s00605-014-0647-x.
15. L. Luperi Baglini, Partition regularity of nonlinear polynomials: a nonstandard approach, Integers, Vol. 14 (2014), A-30.
16. V. Benci, L. Luperi Baglini, Generalized functions beyond distributions, Arab. J. Math, Vol. 4 (2014), Issue 4, 231–253, doi: 10.1007/s40065-014-0114-5.
17. V. Benci, L. Luperi Baglini, Ultrafunctions and applications, DCDS-S, Vol. 7 (2014), Issue 4, 593–616, doi: 10.3934/dcdss.2014.7.593.
18. L. Luperi Baglini, Ultrafilters maximal for finite embeddability, J. Log. Anal., Vol. 6 (2014), A-6, 1–16, doi: http://dx.doi.org/10.4115/jla.v6i0.226 .

Proceedings of conferences
1. L. Luperi Baglini„ Quanti elementi ha un insieme infinito, Atti della X Giornata Nazionale di Analisi Nonstandard per le Scuole Superiori, in publication.
2. V. Benci, L. Luperi Baglini, A topological approach to non-Archimedean mathematics, in: “Geometric Properties for Parabolic and Elliptic PDE”’ (F. Gazzola, K. Ishige, C. Nitsch, P. Salani eds.), Springer Proceedings in Mathematics & Statistics, Vol. 176 (2016), 17–40, doi 10.1007/978-3-319-41538-3_2.
3. V. Benci, L. Luperi Baglini, A generalization of Gauss’ divergence theorem, in: “Recent Advances in Partial Differential Equations and Applications” (V. D. Rădulescu, A. Sequeira, V. A. Solonnikov eds.),
Contemporary Mathematics 666 (2016), 69-84, DOI:http://dx.doi.org/10.1090/conm/666/13335.
4. L. Luperi Baglini, A nonstandard technique in combinatorial number theory, in: “Selected Papers of EuroComb’13” (J. Nesetřil, M. Pellegrini eds.), European J. Combin., Vol. 48 (2015), 71–80, doi:
10.1016/j.ejc.2015.02.010.
5. V. Benci, L. Luperi Baglini, A model problem for ultrafunctions, in: “Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems”, EJDE, Conference 21
(2014), 11–21, ISSN: 1072-6691.
6. V. Benci, L. Luperi Baglini, Basic properties of ultrafunctions, in: “Analysis and Topology in Nonlinear Differential Equations”, Progress in Nonlinear Differential Equations and Their Applications, Vol. 85
(2014), 61–86, 10.1007/978-3-319-04214-5_4.

Long abstracts for conferences
1. L. Luperi Baglini, Partition regularity of nonlinear polynomials: a nonstandard approach, in: The Seventh European Conference on Combinatorics, Graph Theory and Applications (J. Nesetřil, M. Pellegrini, eds.), CRM Series, Vol. 16 (2013), 407–412, doi: 10.1007/978-88-7642-475-5_65.

Preprints
1. P. Arruda, L. Luperi Baglini, Partition regularity of affine algebraic plane curves, submitted, arXiv:2202.04535.
2. P. Arruda, L. Luperi Baglini, Rado functionals and applications, arXiv:2209.07844.
3. S. Goswami, L. Luperi Baglini, S.K. Patra, Polynomial extension of the Stronger Central Sets Theorem, arXiv:2209.10253.
4. L. Luperi Baglini, S.K. Patra, M. Shaikh, Dynamical notions along filters, arXiv:2204.01344.
5. E. Pizzimenti, L. Luperi Baglini, Party organizational development and change: a theoretical framework, submitted.
6. L. Luperi Baglini, P. Giordano, Fixed point iteration methods for arbitrary generalized ODE, in preparation,
https://www.mat.univie.ac.at/~giordap7/preprint_ODE.pdf.
7. P. Giordano, L. Luperi Baglini, A Picard-Lindelöf theorem for smooth PDE, in preparation, https://www.mat.univie.ac.at/~giordap7/PL-PDE.pdf.
8. V. Benci, L. Luperi Baglini, Analisi nonstandard ed applicazioni, in preparation per la rivista UMI.

Other Publications
1. L. Luperi Baglini, Quanti elementi ha un insieme infinito, MatematicaMente, Vol. 293-294, ISSN: 2937-6367.
2. L. Luperi Baglini, Hyperintegers and Nonstandard Techniques in Combinatorics of Numbers, PhD Dissertation (2012), University of Siena, arXiv: 1212.2049.

Most Important Peer Review Activities
I have been a reviewer for the following journals/organizations:
• Journal of Symbolic Logic;
• Combinatorica;
• Journal of Logic and Analysis;
• Mathematical Logic Quarterly;
• Examples and Counterexamples;
• SN Partial Differential Equations and Applications;
• Lecture Notes in Mathematics;
• ANONA;
• The Australasian Journal of Combinatorics;
• Chaos, Solitons & Fractals;
• ”Geometry, Structure and Randomness in Combinatorics”, CRM series;
• MathSciNet;
• Monatshefte f¨ur Mathematik;
• JAMP;
• Soft Computing;
• Mathematics;
• Science Fund of the Republic of Serbia.

Memberships in academic organizations
I am currently the Treasurer of AILA (Associazione Italiana di Logica e sue Applicazioni, Italian Association of Logic and Applications) and I am a member of the IAGF (International Association for Generalized Functions).

Additional professional training
In November 2020–January 2021 I participated in the “Faculty Development RTDB” course promoted by the University of Milan. The course was meant to improve the teaching abilities of RTD B personnel of the University of Milan.