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

 

Contact

Mailing Address: Wolfgang Pauli Institute, 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

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

Present position

At present, I'm a senior researcher at the WPI. This means that to survive, I periodically have to struggle with research project's proposals.
Therefore, 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, Hyperfinite methods.
If you are interested in a new approach to AI that is able to behave in strict analogy with human brain's behavior, see BLS (Sections 1.5, 3.5).
If you are interested in a unifying theory of complex systems, see IS.
If you are interested in a new approach to papers' review, see DistRev.
If you are therefore interested in proposing me a permanent position, we can try an agreement, and this is my CV.
At present, my research projects have been funded for about 1.6 million of Euro from 2002 to 2017.
 

Publications

  1. Lecke A., Luperi Baglini L., Giordano P., The classical theory of calculus of variations for generalized functions. Accepted in Advances in Nonlinear Analysis. Pdf
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  3. Luperi Baglini L., Giordano P., The category of Colombeau algebras. Monatshefte für Mathematik. 2016 DOI 10.1007/s00605-016-0990-1 See MOFM
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  5. 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. Springer
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  7. Giordano P., Kunzinger M., A convenient notion of compact set for generalized functions. Accepted in Proceedings of the Edinburgh Mathematical Society. DOI
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  9. 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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  11. 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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  13. 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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  15. 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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  19. 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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  21. 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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  23. 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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  25. Giordano P., Fermat reals: infinitesimals without Logic. Miskolc Mathematical Notes, Vol. 14 (2013), No. 2, pp. 407–422. MMN
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  27. 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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  29. 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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  31. 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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  33. 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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  35. Giordano P., Fermat-Reyes method in the ring of Fermat reals. Advances in Mathematics 228, pp. 862-893, 2011. ScienceDirect
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  37. 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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  39. Giordano P., The ring of fermat reals, Advances in Mathematics 225 (2010), pp. 2050-2075. ScienceDirect
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  41. Giordano P., Infinitesimals without logic, Russian Journal of Mathematical Physics, 17(2), pp.159-191, 2010. SpringerLink
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  43. 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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  45. 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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  47. 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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  49. 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. Pri
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  51. Giordano P., Infinitesimal Differential Geometry, Acta Mathematica Universitatis Comenianae, 2004, LXIII, 2, pp. 235-278. AMUC
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  53. 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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  55. 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. Ann
  56.  
  57. 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. Ann
  58.  
  59. 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. Ann
  60.  
  61. 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. Ann

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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  3. Albeverio S., Giordano P., Vancheri A. (2015), Modelling and Mathematical Methods for Urban Dynamics. To appear in the Unitext series of Springer Verlag Italy.

Preprints

  1. Giordano P., Zipf's law and Mandelbrot's idea. Pdf
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  3. Luperi Baglini L., Giordano P., Fixed point iteration methods for arbitrary generalized ODE. Pdf
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  5. Giordano P., Luperi Baglini L., Picard-Lindelöf theorem for PDE. Pdf
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  7. Giordano P., A Picard-Lindelöf theorem for singular nonlinear PDE - slides of the talk at ISAAC 2017. Pdf
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  9. Giordano P., Fermat reals: nilpotent infinitesimals and infinite dimensional spaces. Book in peparation. arXiv
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  11. Giordano P., Order relation and geometrical representation of Fermat reals. Pdf
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  13. Giordano P., Katz M., Potential and actual infinitesimals in models of continuum. Pdf
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  15. Giordano P., Kunzinger M., Steinbauer R., A new approach to generalized functions for mathematical physics. Pdf
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  17. Blagowest N.A., Giordano P., Rigorous derivation of Fokker-Planck and Schroedinger equations using Fermat reals. Pdf
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  19. Giordano P. Distributed reviewing - A proposal. Pdf

 

 

Geniuses do not exist. There exist free people:

Leila Schneps on Grothendieck