Teaching
Topos theory course at Insubria
I am currently teaching (in English) a Masterlevel course on Topos
Theory at the University of Insubria (Como, Italy). The lectures have
started on the 2nd of October 2018 and will finish on the 18th of
December; they take place every Tuesday (1618) in the Aula Magna of the
Department of Science and High Technology (Via Valleggio 11, Como) and
every Wednesday (1416: theory and 1618: exercise sessions) in the Aula
4.15 on the fourth floor of the same building.
Slides used as a support for my lectures (regularly
uploaded here):
Lecture 1: Overview of the course
Lectures 234: Categorical
preliminaries
Lectures 56: Sheaves on a topological
spaces
Students from Insubria can access the videos of the lectures at
this link by inserting their credentials.
More information about the course is available at the
course
webpage ; see also these
presentation slides.
Teaching experience
 Lecturer (ongoing) of the course "Topos
theory" at the University of Insubria, Como (Italy), academic
year 20182019
 Lecturer of the course "Algebra
Superiore A" at the University of Insubria, Como (Italy),
academic year 20172018
 Lecturer of the "Topos Theory" course, Master
of Advanced Study in Mathematics at the University of Cambridge
(U.K.), Lent Term 2012 and 2011
Here are the slides that I used as a support for my lectures and the
example sheets of the course. The syllabus of the course is
available here.
Slides:
Lecture 1 
Overview of the course
Lecture 2  Categorical preliminaries I
Lectures 3 and
4  Categorical preliminaries II
Lectures 5 and 6  Sheaves on a site
Lectures 7 and
8  Basic properties of categories of sheaves
Lectures 9 and 10
 Geometric morphisms
Lecture
11  Local operators
Lectures 12
and 13  Geometric morphisms as flat functors
Lectures 14
and 15  Morphisms of sites
Lecture 16 
Points of toposes
Lectures 17
to 20  The interpretation of logic in categories
Lectures 21
and 22  Classifying toposes
Lectures 23
and 24  The unifying methodologies
Example sheets:
Example sheet
1, Example
sheet 2,
Example sheet 3,
Example sheet
4
 Group Leader for the Part III Seminars in Category Theory and Logic, DPMMS,
University of Cambridge (U.K.), 2007 and 2008

Supervisor in Analysis (Part 1A) for students of Trinity College, Cambridge (U.K.)
 Teaching Assistant of Piano at the "Conservatorio di Torino" (Italy), 20052006
Introductory text
Click
here
for a(n unpolished) draft of the first two chapters of my book "Theories,
Sites, Toposes: Relating and studying mathematical theories through
topostheoretic 'bridges'" (Oxford University Press, 2017). This 64 pages text is a selfcontained introduction
to toposes, categorical logic and the 'bridge' technique requiring only
a basic familiarity with category theory.
Researchlevel lecture courses

"Introduction to categorical logic, classifying toposes and the 'bridge' technique", 5hour lecture course
given in English at the conference "Topos à l'IHÉS" (2327 November 2015).
The videos of the four lectures are available
here. The syllabus of the course is available
here.
An edited version of the four lectures with titles for the
various sections (kindly prepared by S. Dugowson) is available
here.

"Toposes as unifying 'bridges' in Mathematics",
18hour lecture course given in French at the
Institut de mathématiques de Jussieu (Universités Paris
67) from the 14th to the 31st of January 2013. This
course, whose
programme can be found here,
was organized by the « Équipe de logique catégorique » and the
« Laboratoire Preuves, Programmes et Systèmes »
of the Paris 7 University;
video recordings of the lectures are available at
this website.

"The unification of Mathematics via Topos Theory", 8hour lecture course given at the Department of Mathematics of the
University of Padova (Italy), 1st2nd July 2010
 "Introduction to Topos Theory and its unifying role in Mathematics",
12hour nationallevel lecture course giving an introduction to
my research work, Centro di Ricerca Matematica Ennio De Giorgi,
Scuola Normale Superiore di Pisa (Italy), 22nd  26th February 2010.
For more information, please visit the
website of the course.