Olivia Caramello's website



"Cohomology of toposes", course at Insubria (a.y. 2019-2020)

This course is given jointly with Prof. Laurent Lafforgue. The lectures take place every Tuesday (14-17) and Friday (13-16) 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. 2018-2019)

In the academic year 2018-2019 I taught (in English) a Master-level 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 2-3-4 - Categorical preliminaries
Lectures 5-6 - Sheaves on a topological space
Lectures 7-14 - Sheaves on a site; basic properties of Grothendieck toposes; local operators
Lectures 15-18 - Geometric morphisms; flat functors; morphisms between sites.
Lectures 19-20 - The interpretation of logic in cateogories
Lectures 21-22 - 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

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 topos-theoretic 'bridges'" (Oxford University Press, 2017). This 64 pages text is a self-contained introduction to toposes, categorical logic and the 'bridge' technique requiring only a basic familiarity with category theory.

Research-level lecture courses