• 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.

• 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 methods in combinatorics of numbers: a few examples, RaTLoCC 2011 - Ramsey Theory in Logic, Combinatorics and  Complexity, Bertinoro - Italy, May 22-27, 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.

• Numerosities: a possible way to refine Cantor's cardinalities, International Congress "Logic and Mathematics", York, UK, August 3-7, 2009.

• 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 special ultrafilters, 10th International workshop in Set Theory, C.I.R.M. - Luminy, September 22-26, 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.

• Euclidean measures of sets, International Congress "Leonhard Euler and Modern Combinatorics", St. Petersburg, June 1-7, 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.

• Set theory and nonstandard analysis, International Congress "Set Theory and Analysis", Turin, July 10-12, 2006.

• I metodi dell'analisi nonstandard (italian), Mathematics Seminars, University of Turin, May 9, 2005.
  

• 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.
  

• Different paths to nonstandard analysis, International Congress "Non Standard Mathematics", Aveiro, Portugal, July 5-10, 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.

• Topological and nonstandard extensions, Joint Mathematics Meeting - AMS special session on ¨Nonstandard Methods¨, Phoenix, Arizona, January 7-8, 2004.

• Topological and nonstandard extensions and their connections with special ultrafilters, International Conference "Logic and its Applications in Algebra and Geometry", University of Michigan, Ann Arbor, April 11-13, 2003.

• Numerosities: a new way of counting, The University of Michigan Mathematics Colloquium, Ann Arbor, April 8, 2003 and  Logic Workshop at Graduate Center/CUNY, New York, April 4, 2003.

• Counting the infinite, Meeting of the Contact Group in Mathematical Logic, University of Mons, Belgium, May 2001.

• A nonstandard set theory where all sets have nonstandard extensions, Conference on "Nonstandard Set Theories and Related Topics", City College/CUNY, New York, December 1-2, 2000.

• Combinatorial principles in nonstandard analysis, Logic Workshop at Graduate Center/CUNY, New York,  November 17, 2000.

• Nonstandard analysis by axiomatic method, Bilgi University, Istanbul, May 2000.

• An elementary presentation to nonstandard analysis, University of Parma (Italy), April 1999.

• *ZFC: an axiomatic approach to nonstandard methods in mathematics, Logic Workshop at Graduate Center/CUNY, New York,  March 13, 1998.

• 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.

• Infinite and infinitesimal numbers: from numerosities to nonstandard analysis, Course for Graduate Students, Sun Yat-sen University, Guang-Zhou (Canton), China, November-December 2005.

Editor

• Member of the Editorial Board of  Journal of Logic and Analysis, starting 2009.

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

• Book: (jointly with V.Bergelson, A.Blass, R.Jin) Ultrafilters across Mathematics (200 pp.), Contemporary Mathematics vol.530, AMS, 2010.

• Book: (jointly with N.J. Cutland and D.A. Ross) Nonstandard Methods and Applications in Mathematics (262 pp.), AK Peters, 2006.

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.

• International workskop on "Infinite Combinatorics", Pisa, Centro di Ricerca Matematica "E. De Giorgi", June 28, 2010. (poster)

• International Congress: ULTRAMATH2008 "Applications of ultrafilters and ultraproducts in mathematics",  Pisa, June 1-7, 2008.

• International Congress: NSM2006 "Nonstandard Methods and Applications in Mathematics", Pisa, May 25-31, 2006.

• International Congress: MARIAN2004 "Nonstandard models of arithmetic and analysis", Pisa, June 25-26, 2004.

• (jointly with A. Berarducci, N.J. Cutland and D.A. Ross) International Congress: NS2002 "Nonstandard methods and applications in mathematics",  Pisa, June 10-16, 2002.

• (jointly with K. Hrbacek) Congress: "Nonstandard set theory and related topics" , The City College of CUNY, December 1-2, 2000. (Sponsored by MAMLS - Mid-Atlantic Mathematical Logic Seminar).

• (jointly with M. Forti) Meeting: "Il tutto e' maggiore della parte?", Centro De Giorgi, Pisa, May 6, 2009. (poster)

• (jointly with M. Forti) Meeting: "Matematica straordinaria: alcuni teoremi inaspettati", Domus Galilaeana, Pisa, December 12, 2008. (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. (poster, programma)

• Meeting: "Il metodo assiomatico da Euclide a Gödel", Domus Galilaeana, Pisa, June 13, 2003. (poster)

• (jointly with V. Benci and M. Forti) Meeting:  "I numeri infinitesimi: aspetti storici, filosofici, scientifici e didattici di una grande controversia", Domus Galilaeana, Pisa, November 15, 2002. (poster)

• 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.

• Fall Semester 2007: University of Hawaii - Department of Mathematics, Honolulu, USA.

• 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.

• 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".

• 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.

• 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).

• 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.