I am happy to give a talk tomorrow at the “Workshop on Semantic Information and Communication” held at the Lagrange Mathematics and Computing Research Center in Paris.
The workshop, which takes place on the 7th and 8th of March, is entitled “Towards a semantic 6G” and gathers experts from different fields whose research can contribute to the development of new conceptual architectures for communication based on semantic information.
As I shall explain in my talk, topos theory is relevant for the goals of semantic communication, and AI techniques based on semantic information more generally, in several different ways. In particular, given the capacity of toposes of embodying the semantics of a great variety of situations, using toposes as ‘bridges’ enables effective transfers of knowledge across different ways of expressing information (formalized as different ways of presenting toposes):
The talk presents an analogy between the role of the Sun in Copernicus’ vision and that of Grothendieck toposes as ‘bridges’ between different mathematical theories, by building on the general notion of a ‘bridge’ object:
On 3 December 2022, the inaugural event of the recently founded Grothendieck Institute will take place at 3:00 p.m. in the Aula Magna of the Mondovì campus of the Polytechnic of Turin. The event, which is sponsored by the Municipality of Mondovì, will be held in Italian and will see the participation of numerous guests, including Johanna Grothendieck (Alexander’s daughter and member of the Institute’s Board of Directors), Laurent Lafforgue (member of the Institute’s Scientific Council), Gino Zaccaria (Professor of Philosophy at Bocconi University) and Nicoletta Sabadini (Professor of Computer Science at the University of Insubria). The round table and the subsequent exchange with the public will be moderated by national TV journalist Francesca Ronchin.
The title of the event is “All’ascolto della voce delle cose. Un progetto visionario per la matematica e non solo“. The expression “all’ascolto della voce delle cose” belongs to Grothendieck himself, who said “Ce qui fait la qualité de l’inventivité et de l’imagination du chercheur, c’est la qualité de son attention, à l’écoute de la voix des choses” (“The quality of a researcher’s inventiveness and imagination is the quality of his attention, to hearing the voices of things”):
Among the topics that will be addressed in the round table, in a way which is accessible to the general public, are basic research and its applications, scientific creativity, the figure of Alexander Grothendieck as an example of the kind of relationship that can exist between scientific studies, humanistic sensitivity and social commitment, abstraction and its relationship with art, ethics in scientific research.
In order to celebrate Jean-Jacques’ work on Copernicus and his reflections on categorial and Grothendieckian mathematics, I shall give (tomorrow at 16.00 French time) a talk entitled “De Copernic à Grothendieck: la puissance du point de vue fecond“, where I shall elaborate on the importance of fruitful points of view in Science by taking as prominent examples the Copernican revolution and Grothendieck’s unifying concept of topos.
For those who wish to attend the conference online, here are the Zoom credentials: