Next week I will be in Domodossola giving a research course on topos theory for the 2022 edition of the International Alpine School of Mathematics and Physics.
The title of my course is Grothendieck toposes, invariants and ‘bridges’. The course will be an introduction to the theory of Grothendieck toposes, with a specific emphasis on the invariants that one can define on them. The point of view that we shall take is the one provided by the theory of toposes as ‘bridges’, which we shall present and illustrate through a selection of notable examples. We shall also discuss the application of these techniques to the investigation and discovery of dualities, equivalences and correspondences in mathematics and beyond.
The programme, which is available from the conference website, is very rich and consists of several contributions highlighting the relevance of Grothendieck’s ideas across many different fields of knowledge.
I will give my own talk, entitled “On the ‘unifying notion’ of topos“, on Friday 27th at 10 am PST (7pm CEST).
A final goal is to implement these techniques on a computer, to automatically generate mathematical results by exploiting the capacity of ‘bridges’ to significantly transform the level of complexity of notions and results. Back in 2010, when I first evoked this possibility in the paper The unification of Mathematics via Topos Theory, that idea was regarded with a lot of skepticism, as something almost too good to be true. Now, the time is ripe to start making that dream into reality.
Thanks again to all our speakers for accepting our invitation or sending us a talk proposal. This has made it possible for us to set up a very rich and varied programme.
We are very happy to have attracted so many people (533 registered participants) to this event, coming from different areas of mathematics, physics, computer science, philosophy and engineering, and also from industry. This illustrates the wide-ranging impact of toposes, and the increasing interest in the subject, across different fields of knowledge.
We hope that this event will further stimulate interdisciplinary research inspired by topos-theoretic ideas, and its applications in different fields. The participants in the conference, as well as any other person interested in toposes, are warmly encouraged to join our community and exchange with each other through the Forum.
Many thanks to IHES and the University of Insubria for their support in organizing this event; the videos of all the talks and course lectures of “Toposes online” will be made available on the YouTube channel of IHES.
We look forward to seeing many of you online and on the forum!