Teaching
"Cohomology of toposes", course at Insubria (a.y. 20192020)
This course is given jointly with Prof. Laurent Lafforgue. The
lectures take place every Tuesday (1417) and Friday (1316) in the room
VA2 in Via Valleggio 11, Como. The programme of the course is available
here.
Slides used as a support for the lectures (will be
regularly uploaded here):
Chapter 1: Basic features of homology and
cohomology
Chapter 2: Categorical preliminaries
"Topos theory", course at Insubria (a.y. 20182019)
In the academic year 20182019 I taught (in English) a Masterlevel
course on Topos Theory at the University of Insubria (Como, Italy).
Slides used as a support for my lectures:
Lecture 1  Overview of the course
Lectures 234  Categorical
preliminaries
Lectures 56  Sheaves on a topological
space
Lectures 714  Sheaves on a site;
basic properties of Grothendieck toposes; local operators
Lectures 1518  Geometric morphisms;
flat functors; morphisms between sites.
Lectures 1920  The interpretation of
logic in cateogories
Lectures 2122  Classifying toposes and
the 'bridge' technique
Students from Insubria can access the videos of the lectures at
this link by inserting their credentials.
The exercises for the exam are available
here.
More information about the course is available at the
course
webpage ; see also these
presentation slides.
Teaching experience
 Lecturer (ongoing) of the course Cohomology of
toposes (together with Laurent Lafforgue) at the University of
Insubria, Como (Italy), academic year 20192020
 Lecturer (ongoing) of the course
Geometria 1 at the University of Insubria, Como (Italy),
academic year 20192020
 Lecturer 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. The syllabus of the course is
available here.
 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.