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CURRICULUM VITAE

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Education
  • October 1995: Ph.D. degree (Dottore di Ricerca), University of Sienna (Italy). Thesis: "Stratified nonstandard universes", supervisors  M. Forti and F. Montagna.
  • July 1990: Degree (Laurea) summa cum laude in Mathematics, University of Pisa (Italy). Thesis: "Direct limits of structures and nonstandard models of analysis ", supervisor M.Forti.


Research interests
  • Mathematical Logic and its applications, Nonstandard Analysis, Ultrafilters, Ramsey Theory, Additive combinatorics.


Invited talks and seminars (selection)

  • Combinatorics of numbers and nonstandard analysis, Universität Wien, April 21, 2016.
  • Introduzione all'analisi con infinitesimi (italian), V Giornata Nazionale di Analisi Nonstandard (Congress on Nonstandard Analysis for high school teachers), University of Verona, October 10, 2015.
  • Ultrafilters and nonstandard methods in combinatorics of numbers, Set Theory Seminars & Models of PA, CUNY Graduate Center, New York, June 18, 2015.
  • Applications of nonstandard analysis in combinatorics of numbers, XXV AILA Meeting (Italian Association of Logic and Applications), Pisa, April 16, 2014.
  • An elementary proof of Jin's theorem, Atelier de travail (workshop) "Les densities et leurs applications", Universite Jean Monnet, St-Etienne, July 8, 2013.
  • Applications in combinatorial number theory of iterated nonstandard extensions and idempotent ultrafilters, CANT 2013 - Combinatorial and Additive Number Theory, CUNY Graduate Center, New York, May 24, 2013.
  • Numerosities: A possible way to refine Cantor's cardinalities where the whole is larger than the part", Colloquium of the Mathematics Department, College of Science, Swansea University, March 22, 2013.
  • Numerosities: a possible way to refine Cantor's cardinalities, Philosophy Department, University of Florence, February 17, 2012.
  • Nonstandard analysis in combinatorics of numbers: some examples, Mathematics seminar - University of Northern Colorado, Greeley, October 4, 2011 & Model Theory Seminar, Graduate Center of CUNY, New York, October 14, 2011.
  • Numerosities: a possible way to refine Cantor's cardinalities, Colloquium of the Mathematics Department, College of Charleston, October 7, 2011.
  • Nonstandard integers in combinatorics of numbers, XXIV AILA Meeting, Bologna, February 2-4, 2011.
  • Model theory and nonstandard analysis (series of seminars, jointly with V.Benci), Summer School in Logic - AILA (Italian Association of Logic and its Applications), Gargnano, August 29-Septemebr 4, 2010.
  • Beyond cardinality: is there a measure for the size of infinite sets  where “the whole is larger than the part”?, Sun Yat-sen University, Guang-Zhou (Canton), December 1st, 2008.
  • Numerosities and fine densities for subsets of natural numbers, XXIII AILA Meeting, Genoa, February 20-23 , 2008.
  • Beyond cardinality: are there measures of sets where the whole is larger than the part?, University of Ghent, Belgium, June 28, 2007 and Mathematics Colloquium, University of Hawaii, Honolulu, September 28, 2007.
  • Ultrafilters and nonstandard models in combinatorial number theory, IIIM 2007 - Incontro Italiano Insiemi e Modelli, Turin, April 2-4, 2007.
  • Numeri infinitesimi ed infiniti: una introduzione critica all'analisi nonstandard (italian), Universita' di Napoli II - Caserta, November 30, 2006 and Universita' di Napoli "Federico II", December 1, 2006.
  • I numeri infinitesimi e l'analisi nonstandard (italian), Olimpics of Mathematics, XXI Italian Final Competition, Cesenatico, May 6, 2005.
  • A new way of counting infinite sets, Mathematics Colloquium, Sun Yat-sen University, Guang-Zhou (Canton), China, December 10, 2004.
  • Infinitely small and infinitely large numbers, Mathematics Seminars, Sun Yat-sen University, Guang-Zhou (Canton), China, November 30, 2004.
  • A purely algebraic characterization of the hyperreals of nonstandard analysis, International Congress: "Logic, algebra and geometry", St. Petersburg Dept. of Steklov Math. Institute - Euler International Math. Institute - Russian Academy of Science, St. Petersburg, Russia, June 1-7, 2004.
  • Counting the infinite, Meeting of the Contact Group in Mathematical Logic, University of Mons, Belgium, May 2001.
  • Nonstandard analysis by axiomatic method, Bilgi University, Istanbul, May 2000.
  • An elementary presentation to nonstandard analysis, University of Parma (Italy), April 1999.
  • Foundations for the use of infinitesimal numbers in mathematics, Seminars in Logic, Philosophy Department, University of Florence, Italy, April 1997.
  • A constructive use of nonwellfounded sets for the foundations of nonstandard analysis , Meeting of the Contact Group in Mathematical Logic, University of Louvain-la-Neuve, Belgium, May 1996.



PhD course


Editor

  • Member of the Editorial Board of the Journal: Logic and Analysis, Springer (2007-2008), journal now discontinued.



Organizer


  • (Jointly with I. van den Berg) Special Session "Logic and Analysis", Logic Colloquium 2013, Evora (Portugal), July 22-27, 2013.
  • International workshop "ULTRACOMBINATORICS - Applications of ultrafilters in combinatorial number theory and related topics", Centro di Ricerca Matematica "E. De Giorgi", January 24-25, 2013.

Italian Meetings:
  • (jointly with M. Forti) Meeting: "Il tutto e' maggiore della parte?", Centro De Giorgi, Pisa, May 6, 2009. (poster)
  • (jointly with V. Benci e M. Forti)  Meeting: "L'infinito in matematica: aspetti storici, scientifici e filosofici", Domus Galilaeana, Pisa, April 22, 2005. (poster
  • (jointly with A. Berarducci, M. Forti and E. Moriconi)  Congress: XXII Incontro AILA (Meeting of the Italian Association of Logic and Applications), held in Pisa, February 10-13, 2005.
  • (jointly with V. Benci e M. Forti)  Meeting: "L'infinito in matematica, fisica e filosofia", Domus Galilaeana, Pisa, March 26, 2004. (posterprogramma)



Research visits
  • AIM - American Institute of Mathematics, SQuaRE on "Nonstandard  methods in Number Theory", AIM Research Conference Center, Palo Alto, August 2014.
  • AIM - American Institute of Mathematics, SQuaRE on "Nonstandard  methods in Number Theory", AIM Research Conference Center, Palo Alto, June 2013.
  • October 2011: Graduate Center November-December 2008: Sun Yat-sen University, Guang-zhou, Canton, China.
  • November-December 2005: Sun Yat-sen University, Guang-zhou, Canton, China.
  • November-December 2004: Sun Yat-sen University, Guang-zhou, Canton, China.
  • Fall Semester 2000: City College of CUNY (City University of New York), USA.
  • June 1998: Caltech (California Institute of Technology), Pasadena, USA.
  • Academic year 1997-1998: City College of CUNY (City University of New York), USA.
  • June-July 1996: NATO Advanced Study Institute (Research School on "Nonstandard Analysis and its Applications"), Edinburgh, UK.



Positions, Grants and Fellowships
  • 2005-2011: Secretary of AILA (Italian Association of Logic and its Applications) 
  • Starting October 2002: Ricercatore (tenured in 2005), Department of Mathematics, University of Pisa, Italy.
  • 2000-2002. Research fellowship (Assegno di ricerca), Department of Applied Mathematics, University of Pisa, Italy.
  • 2000-2001. PSC-CUNY Research Award  (joint research with K. Hrbacek), City University of New York. Title of the research project: "Combinatorial Principles in Nonstandard Analysis".
  • 1998-1999. Italian National Council of Research (CNR) Fellowship.
  • 1997-1998. Italian National Council of Research (CNR) Fellowship to develop a research program abroad. Program developed at the City College/CUNY, New York.
  • 1996-1997. Post-doctoral Research Fellowship, University of Sienna, Italy.
  • 1996 (June-July). Research School, NATO Advanced Study Institute on "Nonstandard Analysis and its Applications", Edinburgh, Scotland.
  • 1992: National competition won for a permanent position as Secondary School Professor in "Mathematics and Physics".
  • 1992: National competition won for a permanent position as a Secondary School teacher in "Mathematics".




Teaching activity abroad
  • 2007-2008 (Fall semester). MATH 244 (Multivariable calculus up to Green's and Stokes' theorems) and MATH 302 (Introduction to differential equations).
  • Report on the observation of my classes by the Mathematics Department Executive Committee of The City College/CUNY, New York: ranked  "excellent".
  • 2000-2001 (Fall semester). MATH 392 (Vector calculus and linear algebra) and MATH 100 (pre-Calculus), City College/CUNY, New York.
  • 1997-1998 (Spring semester) . MATH 90 and MATH 100 (pre-Calculus), City College/CUNY, New York.

Courses taught in Italy:
  • Elementi di Teoria degli Insiemi (Introduction to Axiomatic Set Theory), Ultrafiltri e Metodi Nonstandard (Ultrafilters and Nonstandard Methods), Elementi di Logica Matematica (Introduction to Mathematical Logic), Istituzioni di Logica Matematica (Mathematical Logic), Teoria dei Modelli (Model Theory), Linguaggio e Metodi della Matematica (Discrete Mathematics), Analisi I (Calculus - assistant), Analisi II (Multivariable Calculus - assistant).

Secondary School:
  • 1999-2000, 1994-1995, 1992-1993: Professor at Liceo Scientifico (Viareggio) and Liceo Classico (Viareggio). Courses taught: Introductory algebra, trigonometry, pre-calculus, calculus, basics of physics.