Congresses: click here
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,
StEtienne, 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 24,
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 29Septemebr 4, 2010.
 Beyond
cardinality: is there a measure for the
size of infinite sets where “the
whole is larger than the part”?,
Sun Yatsen University, GuangZhou
(Canton), December 1st, 2008.
 Numerosities and
fine densities for subsets of natural
numbers, XXIII
AILA Meeting, Genoa, February 2023
, 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
24, 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
Yatsen University, GuangZhou (Canton),
China, December 10, 2004.
 Infinitely
small and infinitely large numbers,
Mathematics Seminars, Sun
Yatsen University, GuangZhou (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 17, 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
LouvainlaNeuve, Belgium, May 1996.
PhD course
Editor
 Member of the
Editorial Board of the Journal: Logic and
Analysis, Springer
(20072008), journal now discontinued.
Organizer
 (Jointly with I. van
den Berg) Special Session "Logic and
Analysis", Logic Colloquium 2013, Evora
(Portugal), July 2227, 2013.
 International
workshop "ULTRACOMBINATORICS
 Applications of ultrafilters in
combinatorial number theory and related
topics", Centro di Ricerca
Matematica "E. De Giorgi", January 2425,
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 1013, 2005.
 (jointly with V.
Benci e M.
Forti) Meeting: "L'infinito in
matematica,
fisica e filosofia", Domus
Galilaeana, Pisa, March 26, 2004. (poster, programma)
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 NovemberDecember
2008: Sun Yatsen University, Guangzhou,
Canton, China.
 NovemberDecember
2005: Sun Yatsen University, Guangzhou,
Canton, China.
 NovemberDecember
2004: Sun Yatsen University, Guangzhou,
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
19971998: City College of CUNY (City
University of New York), USA.
 JuneJuly
1996: NATO Advanced Study Institute
(Research School on "Nonstandard
Analysis and its
Applications"), Edinburgh, UK.
Positions,
Grants and Fellowships
 20052011: Secretary
of AILA
(Italian Association of Logic and its
Applications)
 Starting October
2002: Ricercatore (tenured in 2005),
Department of Mathematics, University of
Pisa, Italy.
 20002002. Research
fellowship (Assegno
di ricerca),
Department of Applied Mathematics,
University of Pisa, Italy.
 20002001. PSCCUNY
Research Award
(joint research with K. Hrbacek),
City University of New York. Title of
the research project: "Combinatorial
Principles in Nonstandard
Analysis".
 19981999. Italian
National Council of
Research (CNR) Fellowship.
 19971998. Italian
National Council of
Research (CNR) Fellowship to develop a
research program abroad. Program
developed at the City College/CUNY, New
York.
 19961997.
Postdoctoral Research
Fellowship, University of Sienna, Italy.
 1996 (JuneJuly).
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
 20072008
(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".
 20002001 (Fall semester).
MATH 392 (Vector calculus and linear algebra)
and MATH 100 (preCalculus), City
College/CUNY, New York.
 19971998 (Spring semester) .
MATH 90 and MATH 100 (preCalculus), 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:
 19992000,
19941995, 19921993: Professor at Liceo
Scientifico (Viareggio) and
Liceo Classico (Viareggio). Courses
taught: Introductory algebra,
trigonometry, precalculus, calculus, basics
of physics.
