As a math atheist, I should be excused from this game of genius

 

Contact

Mailing Address: Faculty of Mathematics, Oskar-Morgenstern-Platz 1, A-1090 Wien, Austria

Office: 03.135

Phone: +43 1 4277 50630

Personal eFax: +43 1 4277 850630

E-Mail:

Research interests

  • Nonlinear theories of generalized functions
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  • Non-Archimedean Analysis and Geometry
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  • Mathematical theories of complex systems
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  • Mathematical modelling of complex systems and their applications
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  • Transportation modelling and related decision support systems
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  • Mathematical modelling of urban growth and housing markets
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  • Foundation of differential geometry
 

Present position

At present, I'm a senior researcher at the University of Vienna (temporary position...). Here is my CV.
If you are interested in a new theory of generalized functions which is able to reply from classical theorems of smooth functions to calculus of variation and Grothendieck topos, see IFT, GSF, CalcVar, ODE, PDE, Singular dynamical systems.
If you are interested in a unifying theory of complex systems and its application to artificial general intelligence, see IS, CAS and IS-slide .
If you are interested in a new approach to papers' review, see DistRev.
My research projects have been funded for about 3.05 million Euro from 2002 to 2024. From 2020 to 2024, I'm managing 1'136'000 Euro of funding in five different research projects.
 

Publications

  1. Bryzgalov, A., Islami, K., Giordano, P., Infinitesimal and infinite numbers in applied mathematics. Nonlinear Dynamics, 2024. Pdf
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  2. Giordano, P., Kunzinger, M., Vernaeve, H., A Grothendieck topos of generalized functions I: basic theory. Dissertationes Mathematicae, 592 (2024), 74 pp. DOI: 10.4064/dm230920-7-3 Diss. Math.
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  3. Nugraheni, S., Giordano, P., Generalized holomophich functions: sketches of a new theory. To appear in the volume “Women is Analysis and PDE”, series “Research Perspectives Ghent Analysis and PDE Center”, Birkhäuser, 2023. GHF
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  4. Mukhammadiev, A., Tiwari, D., Giordano, P., A Fourier transform for all generalized functions, 2023. Accepted in Dissertationes Mathematicae, 2023. HFT
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  5. Tiwari, D., Mukhammadiev, A., Giordano, P., Hyper-power series and generalized real analytic functions, 2023. Monats. Math. (2023). https://doi.org/10.1007/s00605-023-01849-8 Springer
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  6. Tiwari, D., Giordano, P., Hyperseries of Colombeau generalized numbers, 2021. Monatshefte für Mathematik, 2021. Springer
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  7. Gastão, S.F., Giordano, P., Bryzgalov, A., Lazo, M.J., Calculus of variations and optimal control for generalized functions. Nonlinear Analysis, 2021. Elsevier
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  8. Mukhammadiev, A., Tiwari D., Apaaboah G., Giordano P., Supremum, infimum and hyperlimits in the non-Archimedean ring of Colombeau generalized numbers. Monatshefte für Mathematik, 2021. Springer
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  9. Giordano P., Kunzinger M., A convenient notion of compact set for generalized functions. Proceedings of the Edinburgh Mathematical Society, Volume 61, Issue 1, February 2018, pp. 57-92. PEMS
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  10. Lecke A., Luperi Baglini L., Giordano P., The classical theory of calculus of variations for generalized functions. Advances in Nonlinear Analysis 2017. ANONA
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  11. Luperi Baglini L., Giordano P., The category of Colombeau algebras. Monatshefte für Mathematik. 2017 DOI 10.1007/s00605-016-0990-1 See MOFM
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  12. Giordano P., Kunzinger M., Inverse Function Theorems for Generalized Smooth Functions. Chapter in "Generalized Functions and Fourier Analysis", Volume 260 of the series Operator Theory: Advances and Applications pp 95-114, 2017. Springer
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  13. Giordano P., Wu E., Calculus in the ring of Fermat reals. Part I: Integral calculus. Advances in Mathematics 289 (2016) 888–927. AIM
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  14. Giordano P., Luperi Baglini L., Asymptotic gauges: Generalization of Colombeau type algebras. Math. Nachr. Volume 289, Issue 2-3, pages 247–274, 2016. MN
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  15. Giordano P., Nigsch E., Unifying order structures for Colombeau algebras. Math. Nachr. Volume 288, Issue 11-12, pages 1286–1302, 2015. MN
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  16. Giordano P., Wu E., Categorical framework for generalized functions. Arabian Journal of Mathematics, Volume 4, Issue 4, pp 301-328, 2015. AJM
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  17. Giordano P., Kunzinger M., Vernaeve H., Strongly internal sets and generalized smooth functions. Journal of Mathematical Analysis and Applications, volume 422, issue 1, 2015, pp. 56-71. JMAA
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  18. Vancheri A., Giordano P., Andrey D., Fuzzy logic based modeling of traffic flows induced by regional shopping malls. Advances in Complex Systems Vol. 17, N. 3 & 4, 2014, (39 pages). ACS
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  19. Giordano P., Caputo P., Vancheri A., Fuzzy evaluation of heterogeneous quantities: measuring urban ecological efficiency. Ecological Modelling 288, 2014, pp. 112–126. ECOMOD
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  20. Giordano P., Which numbers simplify your problem?. Invited contribution for the volume: Mathematics without boundaries: surveys in pure mathematics. T. Rassias and P. Pardalos (Eds.), Springer 2014, XIII, pp. 181-220. Springer
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  21. Giordano P., Fermat reals: infinitesimals without Logic. Miskolc Mathematical Notes, Vol. 14 (2013), No. 2, pp. 407–422. MMN
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  22. Giordano P., Kunzinger M., New topologies on Colombeau generalized numbers and the Fermat-Reyes theorem. Journal of Mathematical Analysis and Applications 399 (2013) 229–238. JMAA
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  23. Vancheri A., Giordano P., Caputo P., A 2009 European index of urban metabolism efficiency, in A new urban metabolism, J.A. Acebillo, A. Martinelli (eds), Actar, 2013. st
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  24. Esmaeili M., Vancheri A., Giordano P., Modeling housing market dynamics using a multi-agent simulation of participants' cognitive behavior. In L. Diappi (editor) Emergent phenomena in housing markets: gentrification, housing search, polarization. Physica-Verlag, 2012, p. 43-83. Amazon
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  25. Giordano P., Kunzinger M., Topological and algebraic structures on the ring of Fermat reals. Israel Journal of Mathematics, January 2013, Volume 193, Issue 1, pp. 459-505. IJM
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  26. Giordano P., Fermat-Reyes method in the ring of Fermat reals. Advances in Mathematics 228, pp. 862-893, 2011. ScienceDirect
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  27. Giordano P., Infinite dimensional spaces and cartesian closedness. Journal of Mathematical Physics, Analysis, Geometry, vol. 7, No. 3, pp. 225-284, 2011. JMPAG
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  28. Giordano P., The ring of fermat reals, Advances in Mathematics 225 (2010), pp. 2050-2075. ScienceDirect
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  29. Giordano P., Infinitesimals without logic, Russian Journal of Mathematical Physics, 17(2), pp.159-191, 2010. SpringerLink
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  30. Esmaeili M., Vancheri A., Giordano P., Mathematical and Computational Modeling of Housing Market Dynamics - System engineering point of view. Peer reviewed conference paper. IEEE International Systems Conference 2010. IEEE
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  31. Vancheri A., Giordano P., Andrey D., Albeverio S., A model for urban growth processes with continuous state cellular automata, multi-agents and related differential equation. Part 1: Theory, in Environment and Planning B: Planning and Design 2008, volume 35, issue 4, pages 723-739. EPB
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  32. Vancheri A., Andrey D., Giordano P., Albeverio S., A model for urban growth processes with continuous state cellular automata, multi-agents and related differential equation. Part 2: Computer Simulations, in Environment and Planning B: Planning and Design 2008, volume 35, pages 863-880. EPB
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  33. Albeverio S., Giordano P., Minazzi F., Introduzione a Matematica e Filosofia, il problema dei fondamenti oggi. Atti del convegno di Mendrisio, 16 novembre 2001. PRISTEM/Storia 14-15, 2006.
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  34. Giordano P., Infinitesimal Differential Geometry, Acta Mathematica Universitatis Comenianae, 2004, LXIII, 2, pp. 235-278. AMUC
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  35. Giordano P., Nilpotent infinitesimals and synthetic differential geometry in classical logic. In Berger, Osswald, and Schuster, editors, "Reuniting the Antipodes - Constructive and Nonstandard Views of the Continuum". Peer reviewed conference paper: see proceedings of the Symposion in Venice, May 17-22, 1999. Vol. 306 of Synthese Library, Kluwer Academic Publishers, Dordrecht, 2001, pp. 75-92. Springer
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  36. Bussotti F., Ferretti M., Giordano P. and Mazzali C. (2000a), A Synthetic Index to Estimate Tree Condition in the Permanent Monitoring Plots of the CONECOFOR programme”, Annali Istituto Sperimentale per la Selvicoltura, Special Issue, Arezzo, Anno 1999, 30, 67–72.
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  37. Ferretti M., Giordano P. and Mazzali C. (2000d), Methods of analysis of the I&C evaluation system. In: Ferretti M. (Ed.), Integrated and Combined (I&C) evaluation of intensive monitoring of forest ecosystems in Italy – Concepts, methods and first results. Annali dell’Istituto Sperimentale per la Selvicoltura, Special Issue, 30: 33-42.
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  38. Ferretti M., Giordano P. and Mazzali C. (2000e), Definitions of risk, status and changes in the Permanent Monitoring Plots in Italy – A preliminary attempt. In: Ferretti M. (Ed.), Integrated and Combined (I&C) evaluation of intensive monitoring of forest ecosystems in Italy – Concepts, methods and first results. Annali dell’Istituto Sperimentale per la Selvicoltura, Special Issue, 30: 135-149.
    39.  
  39. Ferretti, M., F. Alianiello, S. Allavena, T. Amoriello, E. Amorini, F.A. Biondi, A. Buffoni, F. Bussotti, G. Campetella, R. Canullo, A. Costantini, A. Cutini, G. Fabbio, C. Ferrari, P. Giordano, E. Magnani, A. Marchetto, G. Matteucci, C. Mazzali, G. Mecella, R. Mosello, R. Nibbi, B. Petriccione, E. Pompei, F. Riguzzi, G. Scarascia-Mugnozza, M. Tita “The Integrated and Combined (I&C) Evaluation System – Achievements, Problems and Perspectives”. Annali dell'Istituto Sperimentale per la Selvicoltura, volume 30, pp. 151-156, 1999.

Books

  1. Albeverio S., Andrey D., Giordano P., Vancheri A. (Eds.) (2007), The Dynamics of Complex Urban Systems. An Interdisciplinary Approach. Springer, Berlin Heidelberg New York. Proceedings of the conference held in Monte Verità (Ascona) 4-6 November 2004, 350 pages, Physica-Verlag Heidelberg. Springer
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  2. Albeverio S., Giordano P., Vancheri A. (2021), Metodi e Modelli Matematici per le Dinamiche Urbane. Unitext series, Springer-Verlag Italia. Springer

Preprints and some talks

  1. Luperi Baglini L., Giordano P., The Grothendieck topos of generalized functions II: ODE. Pdf
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  2. Giordano P., Luperi Baglini L., The Grothendieck topos of generalized functions III: normal PDE. Pdf
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  3. D. Kebiche, Giordano P. Universal properties of spaces of generalized functions. Pdf
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  4. Giordano P., The Grothendieck topos of generalized functions - slides of the talk at SOURIAU 2019. Pdf
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  5. Giordano P., A Picard-Lindelöf theorem for smooth PDE - slides of the talk at ISAAC 2021. Pdf
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  6. Giordano P., Recent results in generalized smooth functions theory - slides of the talk at GF 2020. Pdf
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  7. Giordano P., Artificial general intelligence based on mathematical theory of complex systems - slides of the seminar at SEAMS-UGM, 2023. mp4 and pdf
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  8. Giordano P., Fermat reals: nilpotent infinitesimals and infinite dimensional spaces. PhD thesis. arXiv
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  9. Blagowest N.A., Giordano P., Rigorous derivation of Fokker-Planck and Schroedinger equations using Fermat reals. Pdf
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  10. Giordano P. Distributed reviewing - A proposal. Pdf

 

 

"La matematica, si no te mata, te trauma", Braian, 9 years old - 18.09.2008, Lima (Perù).

 

Geniuses do not exist. There exist free people:

Leila Schneps on Grothendieck
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