Teaching

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), 2005-2006

"Toposes as unifying 'bridges' in Mathematics", 18-hour lecture course given at the Institut de mathématiques de Jussieu (Universités Paris 6-7) 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", 8-hour lecture course given at the Department of Mathematics of the University of Padova (Italy), 1st-2nd July 2010
"Introduction to Topos Theory and its unifying role in Mathematics", 12-hour national-level 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.